I've got a set of Powertap wheels with the standard 32h aluminum rims. I've had them since around December, and I've persistently struggled with flat tires. Most of the time, they show up the day after a ride. I'll go to the bike to find a tire flat. It's not biased towards front or rear wheel, and I've only had one flat during this time while riding. I've had around 10 flats happen after the fact, all in different spots on the tube, but mostly on the rim side. I've tried four different brands of tubes, checked the tires thoroughly (Gatorskins, they were on a different set of wheels previously and were great), and checked the rims multiple times without finding any sort of metal burs or rough spots. The only other thing I can think of is that the rim tape is a little sloppy and is starting to peel in several spots (on both wheels).

My next course of action is going to be new rim tape, followed by lacing my Powertap to a new rim and calling it quits for those rims. Anyone experienced a similar problem or have any suggestions?

Can't really add anything else.
Punctures on the rim side of tube Narrows the list of usual causes down considerably. Remember your best troubleshooting tools are Patient, Systematic, and Methodical, working of the problem. Now go and get some new Velox on those Bad Boys asap.

That's almost surely it. It only takes a tiny crescent of exposed spoke hole to abrade your inner tube and cause an air leak.

I once spent an hour sanding and scotchbriting a rim to stop the flats. Was using a rubber rimstrip. Didn't work. Got some Velox rim tape. Worked.

Noted and Velox tape ordered. Thanks, everyone.

any kind of irregularity in the rim tape's surface or exposure of a spoke hole can cause a flat. the kind that you are experiencing, after the ride and at home, are not all that uncommon. i think the tube gets abraided from the spoke hole or rough surface of the tape.