98 Chrysler T&C sudden shutdown

When I'm driving on the freeway for a long stretch (200 miles or so), the van will suddenly go from perfect purr to powerless with a gas-rich, backfiring idle. Now here's where it gets weird. If you disconnect the battery (pre-tested) from both cables and reattach, it fires right up and runs like new. Problem is, it could be for 20 miles or another 200. If you do not disconnect the battery, you can only limp along, backfiring and lurching down the Interstate at about 3 mph. Could this be a fuel pump relay, alt relay or somesuch? Or is it an ICM failure? The battery and coil have tested good, and the random failure suggests electrical. The only trouble code I can get off it is the potentially useless -- 12 - Battery input to PCM disconnected during last 50 key starts. Any ideas?