Problem with amp turning on and off?

For some reason my amp likes to turn on and off when it feels like it(kenwood KAC-9104D). No protect light or anything. Just off. It will do this very randomly. I have checked everything, all wiring, everything is in place no shorts. Now I checked the battery voltage when the amp shut off and it read 12.5v, while car was running. People tell me my alt is going because they say no matter what even with an amp hooked up it should be between 13.5-14.4v. Now this is on a brand new battery because I was having electrical problems where if I turned on my lights everything would dim out and the car would stall. Ive had new battery for 2 weeks now and it hasnt happened yet but people insist that my alt is going and its going to happen again soon. Do you think my alt is causing all these problems? Also 1 more thing, about a month ago a nut for my alt mount fell off and the alt was getting knocked around pretty badly, so could that have broken something internally?