Stereo Shuts Off Repeatedly with Vehicle Off

My truck has no alterations to the wiring and everytime I turn my stereo on with the vehicle off the stereo will shut off repeatedly if on anything other than Radio. It never did this before so I was hoping on some info if it may be the Alternator getting weak or something else. Like I said it did all work fine for 5 years prior now its doing this so something is weakened. If I put it on Disc or USB it repeatedly shuts off. While Driving my vehicle if i have the Heater or AC Going and my subs I notice the battery meter drop and the truck sounding like it wants to shut off. 96 F-150 XLT 302 Standard Cab JVC Exad AVX800 2 10" Kicker 07TCVT102 Kicker 800w Amp

Sounds like a weak alternator else bad battery. Or the usual bad connections or (usually fuse-blowing) faulty load. Check alternator output and then battery health.