Several months ago I purchased a 2004 Crossfire convertible. The only mods that I've done was upgraded the headlights and installed led bulbs. Now periodically when I drive the car the radio turns off then back on.
Now within the past several days the radio will turn off when the key is removed and turn back on and change from the radio to the cd player. Today when I got home from lunch when I removed the key from the ignition the lcd went blank. The key fob wouldn't work to lock and unlock the car for several minutes. I had the door open so I put the key in the ignition and turned it on to accessories and the car came on and then I started it. When I started the car I noticed that the clock was reset and my audio settings were set back to zero.

 

Sounds like a battery issue, or a bad battery ground problem.

 

I had the exact same issue back in 2007 when my car was just barely a year old. Chrysler replaced the radio under warranty. (I found out many years later when I upgraded to an Alpine head that the "factory replacement" was actually a repaired unit, based on the sticker on top of the unit.)

 

Many early radios suffered from poor displays, so it seems these were repaired with new displays rather than throw them away, makes sense.