Thanks for your response, PP, but those types of anchors are the exact ones he did use! I guess they also can't stand up to the job. Maybe toggle anchors are the answer?

http://www.homedepot.com/p/Crown-Bolt-3-16-in-x-3-in-Zinc-Plated-Steel-Mushroom-Head-Phillips-Toggle-Bolt-Anchors-15-Pack-10292/100349323

You contractor used cheap anchors, likely the plastic ones that install in holes in walls and expand with the mounting screws. The metal anchors like this:

http://www.homedepot.com/p/E-Z-Ancor-Stud-Solver-7-x-1-1-4-in-Phillips-Zinc-Plated-Flat-Head-Drywall-Anchors-50-Pack-25316/100391938

are so much more reliable.

To use the new anchors, you fill in the old holes, paint over the patches, and move the towel bars a couple of inches left or right. If you don't want to paint and the wall looks to be in good shape, you may be able to screw the new, bigger anchors into the old holes.

So a few years ago, a contractor apparently hung our towel bars with the wrong kind of anchor, so now there are "halos" around each bracket where the drywall is coming loose. What's the best way to go about fixing this--and re-hanging the towel bars? Drywall patch? Or remove a larger section of drywall and reinforcing the studs with a 2x where the towels bars will be? Can this be DIY? TIA!