If your child keeps getting reinfected no matter what you clear, there may be a measurable reason — and the test for it is ordinary, cheap and usually covered.
None of these are exotic. Most pediatricians can order them, and insurance generally covers them.
If normal: you have ruled out an immune deficiency and you can stop wondering. That is worth something on its own.
If abnormal: you finally have an explanation for the whack-a-mole — and in some children it opens doors that were closed, because there is now documentation supporting immune-directed treatment.
The most persuasive line is about the titers specifically: "I want to know whether he actually responds to the vaccines he has already had." That is a concrete clinical question with a concrete answer, and it is harder to wave away than "we want to check his immune system."
Want this answered for your own child? A Plan B synthesis reads every lab and note you have — together — and tells you what is driving the picture, what has never been checked, and what to ask for next.
The first one is free, and you keep the list either way. Phone photos of labs are fine.
Plan B for PANS is written by a parent, not a physician. Nothing here is medical advice or a substitute for your child's clinicians — it is meant to make you the best-informed person in the room when you talk to them.