My 1994 Jeep Grand Cherokee's sound system is acting up. All speakers loose complete sound after about 10 sec.?

Okay, I have just acquired a 1994 Jeep Grand Cherokee that is in excellent condition. The only problem is, however, the stereo is acting up. When I turn the car on, or to ACC, the stereo works fine (all speakers) for about 10 seconds and then fades out to complete silence, as if it has lost power. After about 10 more seconds the stereo comes back on, very faint and distorted and only on the rear divers side speaker. This jeep does have an amplifier so I am guessing it may have something to do with that. The sound system in the Jeep is completely stock, and no modification have been made. I just put a brand new battery in the car and the radio display itself (time, buttons, etc.) continue to work regardless of the speakers malfunctioning. I would love any help or advice about how I could possibly fix this on my own. Like I said before, I believe there is a problem with the amp, and yes the power ratings match the amp's requirements and I have checked all the fuses, but I don't have enough overall knowledge of car stereos to troubleshoot any farther. Thanks In advanced for your help!