HELP!!! - Ignition coil problem on 99 LS1

I'm having an intermittent ignition coil problem with the #5 cylinder on my 99 LS1 where I keep setting codes PO305 and PO355.
I have replaced the entire bank of coils, the individual spark plug
wire and spark plug itself yet the problem doesn't want to go away.
What happens is that the car will run fine for a while and then the #5 coil simply stops working. I thought it might be a broken wire or something but what I've noticed is that if I disconnect the connector to the coil while the car is running and leave it off for 10-15 seconds, after I reconnect the coil it will start working again. This will last for anywhere from 5 minutes to 5 hours before it shuts down again.
It almost seems like it's more of a computer problem than a broken wire because I swear that the ONLY thing I do is disconnect and reconnect the coil connector to clear up the problem.
Has anyone else seen this happen or have any suggestions? Thanks in advance.
Christopher snipped-for-privacy@hotmail.com
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Check the pins in the connector. They could be out of shape, broken or burned.
I have had ignition issues on GM cars before where one pin, or socket in a connector is the fault. Charles
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