Thanks for the replies.
@promidi -- Intel Core i7-4790, 3.60 GHz. The CPU meter barely budges above baseline when running this project.
@gswitz -- I tried everything up to 1024 and down to 128.
@bvideo -- Load balancing was already disabled. I tried toggling it and "Use Multiprocessing Engine" on/off with no effect. By the way, I got an error when I clicked on your link.
My normal practice when I finish mixing a project is to export a 32-bit stereo track and import that into a new project for mastering. That is what I did when this problem surfaced. Just out of curiosity, this morning I tried loading the Adaptive Limiter onto the Master bus of the original multitrack project. With buffers set at 256, the clicks were gone! Not sure what this means, but it argues against the idea that the problem is an issue with CPU or other PC resources.