My bike seems to overheat and shut down

[markie539]

I bought my first bike 2009 GZ250, at first it ran fine but now it shuts down while I am riding it. I took it in to a mechanic and he thought it was the rectifier and battery because my battery was also not holding a charge. I replaced those parts and it still

shuts down. I feels like it is runs out of gas. At first I noticed it happened mostly in 3rd gear, I had a friend check it out and he rode it one in 1st gear and it still turned off. It idles just fine though. I am getting really discouraged because I didn't have much

money to start with and I feel like I am putting more and more into it. Anybody know what I should start to look at to fix this problem?