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It's physically possible.

Put a spherical object in a geostationary orbit, make it rotate about its own axis at a rate suited to your own visibility/non-visibility requirements, and make a portion of it have very low albedo.

Staying at a single point in the sky, the object will only be visible while the higher albedo portion is facing the planet and become invisible while the low albedo portion rotates into view.

It could technically happen by chance but would only be stable for as long as the orbit is stable, which really depends on your planetary system.

You didn't say how far up in the sky you need your object and what type of object you want, so I suggest the plume of a volcano.

Some volcanos and geysers are quite regular in their eruptions. Your volcano will erupt not long after midnight every 24 hours and emit only a short burst of gaseous matter and fine dust-like particles that will drift upward in the still air and remain visible for 18 hours, until the evening wind scatters the cloud and it disappears.

If the eruption is just a short puff, the plume will be a small near-spherical cloud, as this one over Popocatepetl:

Etna even does smoke rings:

A geostationary satellite follows an orbit which keeps it over the same point on the Earth.

https://www.skyandtelescope.com/observing/how-to-see-and-photograph-geosynchronous-satellites/

The streaks are stars which are elongated by the rotation of the earth and the long exposure. The satellites are rotating with the earth and so they look like dots. I was surprised that the satellites this blogger photographed did not track out an analemma like the sun, but he says they stay put.

Unlike the ISS and the many objects in low Earth object, geostationary
satellites are visible all night long every night of the year.

Satellites are technological objects but a thing can be in orbit and not be technological.

If something were bright and in orbit you might be able to see it all the time. You could have it get bright alternately. With satellites these are called satellite flares.

https://en.wikipedia.org/wiki/Satellite_flare

Satellite flare, also known as satellite glint, is the visible
phenomenon caused by the reflective surfaces of passing satellites
(such as antennas, SAR or solar panels), reflecting sunlight toward
the Earth below and appearing as a brief, bright "flare".

The satellites that are famous for this apparently rotate so as to present their reflective surfaces. Something in orbit could be slowly rotating, and when the non reflective side was presented it would seem to disappear to the viewer on the ground.

The Sun of a tidally locked planet, eclipsed by its Moon.

Your people live on a tidally locked planet. The Sun is always in the same spot in the sky.

(Traditionally such planets' habitable zones form a ring with the Sun near the horizon, for practical reasons)

Six hours per day, the Moon passes over, eclipsing it.

Caveats:

• The eclips's start and end are not instantaneous




• The satellite would have to be huge and/or very close for a 25% cover. You'd have to crunch the numbers to see if the system is feasible gravitationally.

This is the equation you are looking for:

$$T^2GM=4𝜋^2R^3$$

This is Kepler's third law, and it correlates mass, semi-major axis length and orbital period.

For a geostationary orbit, you have a circle with a radius of approximatelly 40,000 km. Notice, however, that what the law actually states is that:

The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

Starting from a perfect circular orbit, you can make it elliptical. As long as you keep a semi major axis as long as the radius of a geostationary orbit, your satellite's orbital period will be 24h - but it will have a periapsis much closer to Earth, and an apoapsis much farther. It will look like this:

Bodies always spend more time closer to the apoapsis than closer to the periapsis. That's because their orbital speed is at its maximum at the periapsis and at its lowest in the apoapsis.

Just fine tune the eccentricity of the satellite to spend a quarter of its time closer to tje Earth on the day side and you're all set.

Make Mars go a little faster. Instead of ever seeming to move retrograde for a few months, it just seems to stop for about a day. Decrease their orbital periods and it happens as often as you want.

The planet of a tidally locked satellite.

Your people live in a satellite tidally locked to a gas giant, around a red dwarf.

Similar to, and inspired by (hover to show spoiler)

https://en.wikipedia.org/wiki/Nemesis_(Asimov_novel)

The gas giant looms huge and fixed in the sky. It completely eclipses the star for six hours a day, the "day" being a revolution of the satellite around the gas giant. Having no inner light, it disappears to the naked eye while not illuminated by the star.

When the satellite is between the planet and the star, the planet is still illuminated, as the satellite is too tiny to eclipse anything.

I can imagine a hot-air balloon type creature (similar to what Sagan imagined a living creature on Jupiter might look) that sits up however high you want in the atmosphere but periodically comes down to feed or rest (maybe it feeds on microbes high up in the atmosphere or has ultra stable DNA which allows it to live in higher radiation environments). If you're worried about it blowing around, just make it have an adaptation where it can track itself relative to the ground and is territorial.

The Coandă effect (Wiki)

It's the effect that allows a ping-pong ball to float in a hair dryer. The air clings to the rounded surface of the ball and air pressure magic keeps it in the jet, while the force of the jet itself keeps the ball afloat.

Replace the ball with a sufficiently shaped object (a smooth rock or something) and the hair dryer with a gaseous vent of sufficient strength and you can plausibly get yourself a rock floating (mostly) stationary in the sky for as long as the vent spews. If you want the rock to be higher in the sky, you can put the whole construct on top of a hill and view it from the foot of the hill or some distance away.

Lenticular wave clouds stay in place, relative to the mountain, ridge or other topographic feature that creates them, and they can persist as long as the conditions are favorable. On Earth, around the summer solstice at the right latitude (e.g. London, 51.5 degrees North), you can have around 18 hours of daylight (plus civil twilight, in London's case) for a week or so (the length of daylight does not change rapidly from day to day around the solstices), so the visibility requirement seems feasible. You could even posit a diurnal weather pattern in which, for example, the wind dies down overnight, causing the cloud to dissipate, only to re-form as the wind picks up in the morning.

While geostationary satellites are the obvious answer if orbital altitude is permissible, they don't work in high latitudes.

For these there's a less-stationary but still viable option: a highly elliptical inclined orbit such as a Molniya Orbit or Tundra Orbit, which are designed to give a high dwell time over the area of interest.

This will appear to trace a "γ" gamma-shape in the air, slowing down to essentially stationary and then reversing in the loop:

It spends 2/3 of its time in the small eye of that tail - for the geostationary Tundra orbit, that's the 18 hours you asked for.

With two or more satellites following this same orbit (a "constellation"), you get essentially constant coverage.

If, because of angling of solar panels or something, the satellites are only visible at certain times, such as at the apogee (the very tip of the gamma tail) they can then essentially look like a single stationary object, that periodically blinks out briefly and then turns back on (slightly to one side of where it turned off, but you'd have to be very accurately monitoring it to notice that).

The requested gap of a few hours could either be due to a gap in the constellation, or because to be visible they require the sun to be shining on them, and they are in the earth's shadow at that time.

However, for these to be non-technological would be a stretch. A highly elliptical orbit is feasible though unlikely for a single object, but multiple objects in a constellation, not so much. So, the tricks to make it seem extremely stationary won't work.

Against the sun or stars, though, a single object in a Tundra orbit would appear essentially stationary, rising, hanging there, and setting at the same horizontal position.

Without solar panels, it'd need to be very high albedo - clean white or perhaps crystal?

Polaris already does this, at certain places on the Earth and at certain times of the year.

The title asks for an object while the body asks for a [sic] 'phenomena'; to lean towards the latter we might also entertain:

A rainbow -- you might need to fiddle with the atmosphere a bit, but I think this could be arranged; I might guess something like this already occurs on Earth near waterfalls or that sort of thing.

The auroras -- by which I mean the aurora borealis and the aurora australis -- it seems likely to me that you could fiddle enough with a planet, its magnetic field, and its sun to make these visible 18 hours a day, at least on some parts of the planet. They do tend to take up quite a large segment of the sky.