I have been doing a LOT of work with POE on Juniper products, more specificlly with EX4200, and then soon with EX4300, and I have never seen a port 'flap' in association with POE. I'd highly suggest you open a case with TAC. This could well be something specific to your environment, as in many other places I know of,POE is working as expected, and most of these are {Aruba] AP connetions.
BTW, what versions of Junos are you using on the various platforms? Version will probaby be speciifc to the platforms you listed, as for the 3 listed, a different version of Junos is currently the recommended release for each model.