Our heroes are (or a government is, for all I care) friends with a (seemingly) benevolent superhuman entity. This Entity is quite powerful and can provide various advancements that are used by the heroes, but it is more or less useless for the general public because it could effectively destroy the economy by sharing its advancements and the heroes have kindly asked it not to do that.
Now our heroes face problems and as proper humans are proud to solve them mostly themselves, sometimes with a tip or hint from and often with a gadget given/power granted by the Entity. But now they face a Big Problem, quite possibly an extinction event. The heroes try to fight/solve it and have to retreat because they are outmatched. Rethinking time.
What is a believable reason why they don't ask the Entity to solve their problems? Alternatively: Why the Entity won't solve their problem? (One reason per answer encouraged to avoid list answers.)
- The Entity wouldn't really suffer consequences by not solving the Big Problem, no matter how it ends for the heroes and the rest of the world.
- The Entity would however suffer consequences if it would try to solve the problem. It is not even entirely clear if the Entity would succeed at all and it could, if things comes to the worst, cease existing. Both the Entity and the heroes know that.
- The leader of the heroes (or a majority of them) might just think that putting such important matters into the hand of the Entity might result in it believing it should do that all the time, for the greater good of mankind. And while the Big Problem might be even a problem for the entity, both the heroes and the entity know that subjugating the heroes and rest of the world wouldn't be difficult for the Entity.
- The entity might as well offer sanctuary to its friends/the heroes (only).
Even giving these thoughts I think it is kinda obvious to ask the Entity "Could you please make the Big Problem go away?" and it could reply "Well, I could give it a shot." That wouldn't fit my current narrative and while I could work some way out for the Entity to fail in a humiliating way preventing it to try a plan B, I would prefer if there would be a reasonable scenario where this doesn't even happen.