Stereo Turning itself off?

Well i used to run an old Clarion CD Deck... i ran into some problems with it just turning itself off randomly.  I wasnt sure of the problem but not long after i baught a new Sony Deck.  Had it installed professionally (Best Buy LOL) and everything seemed fine for a few weeks.  Now im getting the same problem i had with the Clarion.  The unit just turns itself off.  However, before it would turn off at any time, now it seems to turn itself off when i touch a button.  When i change any setting (Fm Station, Volume, ect) it turns itself off.  I have also found that it ONLY does this when i start the car... if i touch it within 5 min of starting the car it will turn off.. if i wait a bit after starting the car it runs perfectly fine.  Any ideas on how i can fix this?!?

Here is some info on the car/deck if it will help.

i havnt pulled it out and checked the wires... but heres a new development... basically everytime i apply pressure onto the faceplate it turns itself off..... any ideas?

Sounds like a ground prob., sparkie mentioned the ground strap used by Chrysler/Dodge, in which I have ran across many problems with, what I used to do is cancel out the ground strap and run my own, If you look in the dash, there will be a metal chassis, find a spot and ground it there, I think that would be a good start, and while you have the deck out, like sparky said, put a voltmeter on your +12V and switched power to see if any of those are dropping out, if so, then go to the fuses and check contacts, or if there is any build up on the fuses, I have actually seen cases with vehicles where people smoked in them and after time, it creates a nicotine build up on fuses, where all you have to do is clean the contacts or replace the fuse and the problem is solved!! Funny, I didn't believe it till I saw it!!