I would turn the eyes off on my BL Closer all the time playing, I hated that. Wouldn't turn my gun off, but I used to hit the on/off switch on my droid all the time with the elastic band of my barrel sleeve, resulting in me shooting in the sleeve, drove me nuts lol.
I'm assuming that the gun is turning off without you depressing the button? Am I interpreting this correctly? Which gun is it anyways? The Drone DX and Clone GT are the only ones that come with the DX style membrane pad, which takes a little more force to depress the button.
Since I assume it's not due to depressing the button though, I'm guessing the battery may be losing constant contact with the battery connectors on the board. Over time those connectors can bend (since you didn't mention which type of gun it was I'm going down all avenues since this type of thing typically only happens with older guns that have been used for a while). If the battery is losing contact with those connectors, you can shim the area between the bottom of the battery and the frame. People have had success using something about as thick as a credit card.