Nights getting colder, perhaps?

FataMorgana

I'm not sure why this is happening but I know when plants start to flower, they're using up lots of energy and nutrients in the process. Perhaps a little bit of fert might help? And, if you won't be using all of the blossoms (for seed saving), then I suggest you snip most of them off. The plants may perk up after that.

There have been some new stems that have popped up and those are dark green. I'm going to snip off the blossoms and see what happens.
Thanks for all the comments.

I try to keep all the flowers removed as long as possible on basil, to keep them producing better leaves. They get really determined, though, and will eventually work to bloom despite efforts to the contrary, which is usually a sign that they are done for the season. This is a good reason for succession planting, starting basil every two weeks or so in smaller batches, so that when it starts flowering you just harvest and remove the whole batch, reseeding once they are removed.

remove the basil flowers will side new shoots will more grow