The rollers are a standard sort of item: a nylon wheel on a metal hub. This was the worst of the four, with the hub nearly rusted away. The other door is in the background, with a somewhat less-worn roller, but we decided to replace all four of them.
Replacing the worn-out rollers should be routine and relatively cheap, except none of the stores around here actually carry this routine and cheap part. Oh, sure, we could order it and wait a week and spend more on shipping than the cost of the part. In the end, we decided to go ahead and buy two shower-door hanging assemblies ($10 each) that contained a lot more than we needed, but did each contain two of the nylon wheels. As far as the cost goes, it's nearly a wash (ahem) when you factor in shipping costs and waiting time for a part that was on the point of failure.
The old rollers were so rusty that Lisa had to use her Vice-Grips to free up the screws and remove them. Disassembly the new assemblies to get at their nylon wheels was hardly any work at all, and the new wheels were easy to reinstall in the old door. Lisa also took the opportunity, with the door disassembled, to clean the top rail before we put all of the parts back together and lifted the rail-door assembly back into place in the shower.
The old doors now roll with the push of one finger, and quietly, too. Given that they've always rumbled, they probably weren't in great condition when we bought the house, so with luck we will have a long time before we have to repeat this exercise.
I'm grateful for Lisa diagnosing this so quickly. I'd still probably be trying to figure out how to get the doors out.