The herbs that you've mentioned are all full-sun loving plants. Have you checked for spider mites?

I don't see any of the usual indicators for spider mites, but perhaps I'm missing them on the rosemary. (The parsley and the basil are doing fine at the moment, other than some aphids on the parsley.) All the others I mentioned are dead and gone already.

Any particular way to check for mites on rosemary?

I realize these are full sun - but could it be too much sun? Would the pot matter? Sometimes I wonder if the roots end up baking in the plastic pot in the sun.

"Any particular way to check for mites on rosemary?"---if you see that the leaves have become stippled, yellow, and dry, and has fine webbing, chances are your rosemary has mites....How many hours of sunlight do they receive? Do you water them every so often? How about the nutrient dosage?

Leaves are yellow (or brown tipped) and dry. You might call them stippled too, but I'm not sure on that. But no webbing.

They receive 12-14 hours of good light, with probably 8 of that being direct blazing sun.

I water when a dowel inserted in the soil comes up dry. Every few waterings they get a dose of a balanced (NPK + assorted micro nutrients) fertilizer.

Until I figure out what's going on, I gave the rosemary a spraying of water (including as much as I could, the undersides) that might dislodge pests and moved it to a less bright window.

I'm not sure by any means, but you may be onto something when you mention heat. A southern window can get quite hot, and your plants' roots may be cooking. Is there a way for you to "double pot" them, perhaps putting the smaller pots inside bigger pots with something to insulate them from the sun's heat? Something as simple and cheap as plastic packing peanuts would probably make a fairly good insulating barrier. It's at least worth a try... Good luck!