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With hydraulic control surfaces, at high airspeeds, there is a point where aerodynamic loads exceed the capability of the actuators. This limits control authority and can result in the control surface not being in the position commanded by the pilot.

Jackscrews are commonly used for horizontal stabilizer control. I know they can jam and be difficult to move under high loads, but can they be blown back from their set position or do they stay put?

Screws can be either self-locking or overhauling. Jackscrews used for stabilizer control are designed to be self-locking, since their purpose is to make the stabilizer adjustable, but prevent it from moving by itself.

A jackscrew (or screw jack) is pretty much by definition a self-locking screw.

Wikipedia: Screws - self-locking property

Acme screw type screw jacks with the square threads, as used in stab trim systems (as opposed to recirculating a ball screw), are usually inherently irreversible because of the higher friction of the direct sliding contact of the square sided threads vs a rolling ball interface (as a sliding interface, it's totally dependent on the grease to keep friction in check).

This is why the trim screw jack of the 737 becomes extremely difficult to move manually when the jack is heavily loaded, even though the movement input is coming from input side that is supposed to be the low effort side, requiring a technique of unloading it with elevator inputs to manually trim when the airplane's actual speed and trim speed are far apart.

Ballscrew type jacks however, typically used for flap actuators, have very low internal friction and very high efficiency thanks to the ball interface between the "nut" and screw (rolling, not sliding). As a result they can be back-driven more easily; how easily depends on the gear reduction within the worm drive gearbox.

Ballscrew operated flap systems typically require friction brakes in the drive line, or anti-backdrive devices incorporated internally in each actuator (basically a clutch device that is disengaged only when the torque is coming from the input side), to prevent a flap surface that is disconnected from its drive motor from creeping up from air loads.

Acme screw actuators also have internal brakes but these mainly function to lock an inoperative motor when there are dual motors, so that the live motor can't backdrive the dead one instead of the downstream gear train. They also serve to lock the acme screw when both motors are off, but this isn't as critical with an acme screw.