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I find myself often being irritated at elements in situations that help characters succeed, elements which are also highly unlikely or even illogical. But often, if not more, I find myself angered by things that too inconvenient. Improbably inconvenient. But am I alone on this? Is it a pedantic irritation or is unlikely inconvenience bad writing?

To be very clear: (a Fantasy setting) If characters are fighting a fight they'll never win, and a never before mentioned/foreshadowed/hinted at dragon swoops down and saves the day, that would be too convenient.

Oppositely, if the characters are winning the fight, but that same dragon swoops down and makes them lose, that would be too inconvenient, at least in my opinion.

Now, if I understand correctly, there are multiple components to this: The dragon hasn't been mentioned, for the dragon to appear is very unlikely and the dragon is irrelevant to what is happening (the fight). I believe there is small differences in inconvenience based on which of these three it suffers from. I'll tackle them in order.

In a book I was reviewing, there is this whole species that is enslaved secretly by some bad people. A resistance freed the species, and chose to hold them in airplane hangars, waiting for whatever, not important. The resistance had not planned ahead enough though, and neither had the author. The main character let's us know that "OH NO! You have all the males in one hangar together? If they are left like that, they kill each other!". Have in mind, this was the second last chapter.

So, this is a problem, and it comes out of nowhere, because it is based on never before mentioned information. To me, it comes off as cheap. Imagine someone is attacking the airstrip, and instead of kill each others, when the males are in the same room, they all give each others superpowers, and are therefore conveniently able to repel the attack. There could be a smart and scientific explanation to this, but it wouldn't matter, because if it hadn't been mentioned before, it would be cheap and too convenient.

Then you have inconveniences that are just very unlikely. Imagine our hero is chasing the villain, and he is close to catching him, and then he is struck by lightening. Too inconvenient. Also, this inconvenience suffers from the last one too, it is irrelevant. Unless the villain has superpowers or is a god, it is completely irrelevant to the story and the conflict in question that the lightening would strike our hero. Now, if there's a thunderstorm, these people are on top of a mountain and they have giant metal poles attached to their heads, then sure, it is a little less unlikely. Perhaps even more likely to happen than not. But relevant?

Though I must admit, I am very unsure in this "theory", as I have witnessed inconvenience and liked it, like in Whiplash, where the main character is hit by a car before attending the concert he was supposed to play at. Though, he was speeding, lowering the unlikeliness, car crashes are a widespread phenomenon, so it doesn't require mentioning, but is it irrelevant? From a narrative perspective, perhaps not?

Anyways, one thing is for certain, if convenience suffers from any of the aforementioned things, then it will not fly. But is it tolerable for inconvenience? My core question is really this:

Is there narrative-wise an inherent difference between convenience and inconvenience, making it so that the same rules don't apply to the latter?

The twin tropes you are referring to are Deus ex Machina and Diabolus es Machina. In both cases an event comes out of nowhere, not foreshadowed, to effect a drastic change.

Both tropes are frowned upon. For example, Marion Dane Bauer in her book on writing, would say to her writing students "If you end your story by having your main character get hit by a truck, you have just flunked." (taken from the above tvtropes link, didn't find original source)

There is a little more leeway with inconvenience than with convenience: an additional challenge for the characters to face is more interesting than the challenge getting solved all by itself. Nonetheless, "things going wrong" would usually take the shape of "everything that could go wrong, goes wrong" - things that are plausible within the story. (On the flip side, if everything goes according to the best-case scenario, it's a bit underwhelming.) A problem that comes out of left field, particularly in the last part of the novel - it's not a good thing.

I would say anything that seems to come out of nowhere is unrealistic fiction, unless the fact that it comes out of nowhere is fairly concealed.

For example, I can make my protagonist's father a college professor, and her mother an MBA business manager, and because of that she knows some stuff critical to the plot about both academia and business that the average person would not know.

Now, her knowledge is justified, but in the story, her parent's professions were not justified; she was just born with the parents she has. But if I write it correctly and early readers won't care how convenient her parent's professions were.

On the flip side, in The Hunger Games (movie), Mrs. Everdeen is in a deep depression, and this is the reason Katniss becomes the stand-in mother and provider for her 12 year old sister, Prim, and it is in this role that Katniss volunteers to take Prim's place in The Hunger Games. The entire plot hinges on Mrs. Everdeen's unexplained and inconvenient depression, or at least Katniss's love for her little sister. (In the book the depression is caused by the death of their father in an inconvenient mining accident.)

In short, I want to say that everything can be traced to some good luck or bad luck in our character's lives, so we don't have to go too deep in order to hide that, and make the luck once or twice removed.

If I really want a victory to be upended by a dragon my heroes did not expect, it is easy enough to plant the seeds for that as early in the book as I like. At the beginning of the quest, they stole something from the dragon in order to begin their quest. Or they were (randomly) attacked by a juvenile blue dragon, and killed it -- the child of a much larger blue dragon that has been seeking revenge ever since.

Plots demand both successes and failures. Both of those should be justifiable, and the more important the success or failure, the more "layers" of justification should be used to disguise the fact that in the end, it was luck.

The luck of being in the right place at the right time, the luck of being born with the right skill or to the right parents, the luck of searching for the right thing instead of the wrong thing, the luck of random decisions working out. Or the bad luck of any reversals of the above, and perhaps the character's responses to such hardships, which turn the hardships into advantages: Katniss Everdeen, again, becomes an expert huntress and markswoman because of her mother's disability and the need to step up and provide for her baby sister; and the inconvenient illness of her mother conveniently gives Katniss exactly the expert skill she needs to survive the Games. (Not to mention it is very convenient that the one enemy killed by Tracker Jacker wasps is the one with the bow and arrows, something entirely unplanned by Katniss).

I would fall back on Sanderson's First Law of Magicks

Sanderson’s First Law of Magics: An author’s ability to solve conflict with magic is DIRECTLY PROPORTIONAL to how well the reader understands said magic.

Magic, of course, has similar writing properties as convenience might. I think the key wording is "ability to solve conflict." It doesn't matter who wins in the conflict, its the fact that it is solved which causes the issue.

Consider the difference between a dragon that suddenly swoops down and resolves the fight between the hero and villain, and a dragon which comes down, ruins all of the potential resolutions available, perhaps steals a princess before returning to their lair, leaving both hero and villain scratching their heads about what to do. Now the conflict hasn't been resolved, but rather a whole new aspect of the world has been exposed.

Of course, such a move does resolve some conflict, so it is up to the author to convince the reader that it's a good trade -- the conflict they knew and were comfortable with, traded away for this shiny new unknown conflict!