I have a friend with a 87 Gt that just had the 3.4 motor rebuilt about 4000 miles ago and a swap to a 440t4 at the same time.
The proublem is every once in a while after the car is warmed up and then shut off (to go in to the store or what ever),when he goes back to start the car back up ,it act as if their is bearly any power to start the car some time not enough,as if the battery is weak .
Got a battery thats 550 cold cranking amps and is good ,Only about 1 year old .
New ACDelco alternatar and starter were also put on the car at rebuild.
Anything else he should look for that would cause a low power input everyonce in a while to the starter.

A bad ground cable or a loose connection could cause those symptoms.

I agree, check the cables. They can often increase resistance at the connections when they get hot. Make sure the battery connection is tight.
Best check would be to measure the voltage at the starter to ground when cranked to see what it is.
If you have 12v then could be the starter has a heat issue.

[This message has been edited by Dodgerunner (edited 03-09-2009).]

Thanks for the info ,I should have mention the battery was reloctaed to the front,so the battery connections should be looked cat very close