Thanks for the advice guys. mph medic, I'm definitely with you on trying to make the existing roof last as long as possible. I've not yet removed the gutters to see what's going on at the edges, but it seems that the loosest spots are towards the center. I don't think it's a situation where I can say lift up the front third of the epdm, glue and replace...I think I'm dealing more with several large "spots" that are coming loose. I don't know if there's anything like this out there, but what I had in mind was injecting some glue under the membrane with a syringe or something, then repairing the hole(s) with eternabond.
sharker, I think that mechanically fastening my loose spots might just be the way to go. Of course I'm always nervous about putting MORE holes in the roof, but I could put a large eternabond patch over each fastener and probably be ok. Maybe I can come up with some way to do a combination of mechanical fasteners and injected glue.
Thanks for the quick responses!