I used to own a 91 LeBaron with the A604 transmission. From chit-chat on the internet I get the impression that these transmissions need rebuilding every 80,000 miles. Though the input and output sensors may often cause the limp-home problem, it's still pretty much up in the air what could cause the problem. Nobody seems to have nailed down a 'common' problem for this transmission. C32AMG is correct in stating that the first step for diagnosis is to read the CVI's (clutch volume index) and codes.
I would think hard before tackling the A604 for a rebuild project. These transmissions require many special tools, plus there have been many upgrades. A good trans rebuilder would know these upgrades. The trick is finding a good rebuilder. Try cruising the
Allpar forum. Lots of knowledgeable people there. You should get some good recommendations.
If you insist on doing it yourself, I still have the complete factory shop manual for '91 Chrysler FWD vehicles. The A604 Ultradrive section has 64 pages.