I had a PET/CT scan just under three months out from treatments, then another one 2 months later, due to what turned out to be false positives on the first one. Both ordered by my MO. My ENT/Surgeon and my RO are not enthralled by scans.
I am coming up on the one year anniversary of the second scan, but have not yet heard anything from any of the 3 about a repeat, and I just had my latest checkup with the ENT/Surgeon yesterday. I see the RO in December and the MO again in early January, so maybe he will order one then.
As you can probably gather, this is a highly individualized thing, depending upon the institution and the treatment course.