I'd get a new battery first, if that doesn't make a difference in the running then it'll probably be a clogged fuel tap, that's what happened to me like two weeks ago. I had cleaned the carb and my electrical problems went away with the new battery but my bike would cut out and refuse to start again, and it would run like doggy do when it did run. After a few minutes it would cut out and not turn on again. Mine was made in 1996 and has been on the road since 97, on and off.
Check the fuel tap by turning it "off" pulling the rubber hose off it and then switching it to "on" with a little jug to catch fuel.. if the fuel doesn't flow like your household sink's tap then it's clogged up in there. Mine wouldn't flow at all unless I shook it like a ragdoll.
The branded Keihin fuel taps on these european models here are crap, they can't be disassembled. However, you can still pull them out the tank and blast the internal filter (straw looking thing) through with carb cleaner. That did the trick for me, no issues since. You'll see a bunch of crud in the straw, dunno where it came from in mine cuz the tank is pristine when you shine a torch in there. To be expected though since it rolled out the factory some 24 years ago.
Interestingly enough I did leave the bike sitting for a month or two this winter, that was probably enough to let any crud floating in the fuel to settle at the bottom and stick to the fuel tap assembly
1997 Honda CA125 Rebel