The maximum amount of time I can usually last in a single session is usually an hour for short games. For games the lasts longer than an hour, I can usually last for as long as the run itself, or I can only crank out very few attempts in a single session.

This is more of a mental problem btw, I still have energy but after an hour, I just became mentally weak to squeeze out more attempts

Are you asking how to build up stamina, or how to address persistent mental fatigue?

For the former, just practice more. Take breaks as needed, but see if you can do a little more each time.

For the latter, meet with a physician.

Also, make sure you’re getting enough sleep at night.

Let me go into detail here, let's say I lose a run after an hour of attempts, I would start feeling discouraged and I lose my motivation. I will tell myself "This is so fucking stupid, I would never get a run, WTF's wrong with me, etc." (You get the point here)

Is that enough explanation?

Like most things in speedrunning, bouncing back from a painful miss tends to get easier with experience. Keep pushing, keep improving, lose faster and faster runs in stupider and more ridiculous ways; with any luck you'll get accustomed to it, and even if you don't, you'll still forget all about the original lost run that was so disheartening at the time. Eventually the good run will happen; and the more attempts it took, the faster it probably ends up being.

If it doesn't work that way for you personally... just get the good run in that first hour. This isn't an entirely flippant answer; there are incredibly good speedrunners who've consistently played a game at a high level for years, still lose heart after major setbacks, and just work around the problem by basically being better at the game than everybody else. You don't need an unflappable and permanently upbeat attitude to be good; sometimes, champions are champions precisely because of how intensely they hate losing.

That said, both of those approaches work best if even under all the discouragement, the prospect of that one good run still motivates you. If you stop wanting the good run at all I cannot help there, beyond saying "take a break and do something that does motivate you."

Don't try to force it, if you don't feel like more then don't, shorter sessions do have their benefits too (and to be perfectly honest none of my better runs ever came out of longer sessions) and it's really not worth inducing even more stress into a hobby that can already become very stressful. That said if motivation becomes a recurring problem even before starting the session then consider switching entirely to practice for a while / a category change / another game / a break from speedrunning altogether (in that order).

If you find yourself getting very demoralized, (something I've found to be common with longer runs), then you just need to convert that negativity somehow. If you've lost a run, instead of dwelling on it use that run as motivation to continue improving yourself- always aiming make sure that you never lose a run like that again. Life's all about making mistakes and learning from them, and speedrunning is no different. Look at the mistakes you made in a failed run, and practice whatever you need to so that you don't make those mistakes again.

Sometimes it's like a war of attrition. You're not going to see rapid successes, but only small victories spread about until you hit some breakthrough point. The big runners with their legendary WRs have lost thousands upon thousands of attempts sometimes, and all of those are part of the journey to the top.

If all that sounds annoyingly positive, I get it. I'm the type to dwell on the smallest of problems and I don't always follow this advice in the moment. It helps when I do remember to, though.

Also, as a general thing for long runs, it helps to keep saves at different points, at least one near the end and maybe one near the midway point. The longer a run is, the less often you'll be experiencing the later segments thanks to resets. A segment less practiced is one more likely to fall apart and cause more resets. If you want to get more advanced with it, keep some saves that are in a somewhat troubled state so you can practice backup strats.

Run smarter, not harder.