1. It would obviously be quick and easy for the other person to do the thing, and would be significantly easier for them than for me at this time. Examples: While you're up, could you get me a glass of water? Since you're taking the car to visit a friend who lives near the pet store, can you pick up dog food on your way home?
2. I am incapable of doing the thing, and the results if the thing does not happen would be awful. Examples: I am really, really sick and just cannot manage walking the dog. I have an important meeting at work but someone needs to be home to meet the repairman.
So there is this enormous missing range in the middle, where it is hard for me to do a thing (but not completely impossible), and the results if it doesn't happen would be bad (but not necessarily catastrophic), and the thing would not be trivial for someone else to do (but might still be easier than it would for me). If there is no time pressure on these, I can usually work around to asking for help if I need/want it, but when I am sick or otherwise partially incapacitated it is extremely difficult for me to ask for help with daily or already-scheduled things, especially when the people I could ask are also sick or busy or otherwise dealing with whatever it is that's got me functioning at less than full capacity.
Partly this is because explaining the task, in enough detail for the other person to do it, can be more effort for me than just doing it, because of how my brain works (my introversion, let me show you it). Partly this is because I do not have a simple way to compare how difficult it is for me to do a thing with how difficult it is for the other person to do the thing, and I only want to ask if it will be easier for them than for me. I think this second part is probably broken. I mean, (1) it is not actually a moral imperative to create maximum total easiness at all times, (2) even if it were, I am not the only person who can do the comparing-relative-ease work, (3) "no" is a possible answer, if the other person would rather not do the thing.
On the other hand, if the other person says "no", then I have just wasted all this valuable energy I could have spent doing the thing on finding the person, explaining the thing, asking for the thing, maybe discussing relative energy levels for a while... which is all clearly suboptimal. So minimizing "no"s seems like a reasonable strategy to conserve energy, except that then I am missing out on some "yes"es that would save me more energy. But the task of calculating the probability of "yes" times the amount of energy saved, with consideration for the amount of energy spent on asking and careful examination of the amount of energy I actually have, is really a lot of work. I don't have a simple bright line other than the near-certainty of getting a "yes" in the situations outlined above, so when I don't have the time to sit down and work out the calculations, I default to not asking.
What heuristics do you use to decide when to ask people for help with things?