Could be but the symptoms he describes sound exactly like a bad module. They will work fine until they heat up then crap out until they cool off after 20 or 30 minutes. Either way, two good places to start looking and two easy checks. Remove the vacuum line as suggested and if it still dies, unbolt the module from the fender and get it tested at your nearest parts store.
'84 CJ-17: 17" stretch, locked Toy axles, 5.5" lift, FI, AX15, D300 w/twin sticks, boatsides & junk.