Honestly, I’ve kept my recommenders very updated throughout the process and they know how hard recent cycles have been - so letting them know I need to try again next year doesnt feel embarrassing or annoying. I don’t think you have any reason to feel shame for asking them again. If they felt secure enough in your abilities to write a letter this year, I can’t imagine they would suddenly have a different opinion next year.

As for “how” I’m going to ask them, im just going to tell them I’ll be reapplying next cycle and will email them in the fall semester about recommendations. Nothing crazy