Posting a follow up . . . I did swap out the Infinity head units . . . put the HU from my coupe into the rescue roadster and I still have the same problem with the sound cutting out after a while. Per advice from GraphiteGhost, I am going to check out all the wiring to / from the amplifier and also to the speakers. Another clue is that I noticed today that the right door speaker is crackling and has a bit of static. Hope I can spot something obvious because if not, I won't know what to do next.

I've decided to install a Sony radio with a 7" flip up screen and also a back up camera. I was luckily able to buy the same radio as seen in this recently sold SRT6 roadster.

http://www.ebay.com/itm/2005-Chrysler-Crossfire-/221746529201?ssPageName=STRK%3AMEBIDX%3AIT&_trksid=p2047675.l2557&nma=true&si=7Nc2oKV8DfPFcWHsZeeYrqVlK3M%253D&orig_cvip=true&rt=nc
I certainly don't want to go to all that effort and expense and still have the original problem with the sound cutting out. Any other thoughts??