This might have nothing to do with it, but my buddy did a 4.0L swap on his old jeep. When he got it fired up it would run for ~30sec than die. Turned out that the computer thought it was stolen, and would not allow the engine to run any longer than that.
Does it sputter and die, or does it seem to run fine? Can you rev it up in that minute?
I am wondering if the computer is shutting it down?
PZ