Have you tried a complete reflash? Have you removed your SD cards (both of them?)

Sounds like something in your initfs is b0rked and/or [without knowing anything about the boot process] perhaps a fsck is being run and breaking on corrupt SD cards.

After reflashing and starting for the first time - does it continue the 3 minute power cycles?

I certainly wouldn't keep any hardware that only let me power on every 3 minutes [i.e. get it replaced!]