The default switches on import joysticks aren't the best. It's possible that one of them is flaky.
The first thing you should do is switch your wiring around, from one stick to the other, and see if the issue follows the wiring or the joystick. If it's the joystick, then it's probably one or more of the switches that isn't working well. If you want to try to save the wonky switch, you might be able to open it up and get some contact cleaner in there. But this isn't for the faint of heart. Lots of small, spring-loaded parts, which like to pop out of place and take a bit of patience to get back properly.
Also, with this style switch, you can adjust the metal levers. Again, the lower quality switches may have an actuation point which varies between switches, and adjustment of the lever may be helpful.