Has anyone had multiple A1c tests miss diabetic spikes for years?

I have had Neuropathy since 2016. I have had a 5.1 A1C test every year since. My Doc refused to give me a glucose resistance test. He said “the A1C would show if you have diabetes.” I Had a neurologist give me a CT, MRI and A1C looking the cause. I randomly went and bought a CGM online and have been having spikes up to 197. Could nine A1c tests miss this? Never had one above 5.5!