
My American cocker is on soloxine for hypothyroidsm. He was tested 2 months after diagnoses, another 2 after that and now it'll just be when necessary, probably yearly! As his most acute and obvious symptoms when hypo are behaviour issues (aggression), it would show very quickly if something is out of sink in his case!
Personally I wouldn't be happy with three-monthly tests unless necessary as Jesse hates bloods being taken, so it would just put unnecessary stress on Jesse, me and the vet!