With an automatic, there is also the 'pulse module' involved.
It is located inside the under hood fuse box and serves to initiate the starter when commanded.
It serves two purposes :
1. stops turning the starter when the PTCM tells it the engine is running ( if you continue to hold the key in start position )
2. stops turning the starter after about 10-15 seconds if the engine does not start.

There was a forum member back early this year who found that one of the harness wires from the PTCM to the pulse module was intermittent. He was experiencing the same symptoms as you.