Did you lose the bat? And is the sniper infected...? Anyway, I just tested it and found a bug. If you enter the sniper fight without any additional looting after getting the initial throwing weapon and bat, the battle becomes unwinnable and you get stuck. I will get this fixed.
The bat doesn't attack it only make throwables a 100% accurate, so use the items like baseball and such to deal damage, you can attack 2 times then defender. (Hope ir helps)