Have you been keeping a diary of how often, and how long it last?
Best will in the world, if you go and see a GP in isolation and say its happened before there is no evidence to do more. Show evidence that this is more than just a random event.
Plus the fact that virus causes temperature, not just infection, infection takes time to clear, not just 2-3days, and when kids get infected you normally know about it ie they don’t just go back to school. The fact she gets a temperature and then doesn’t get infection is a good thing.
But yes I can see your frustration. Keep a diary, and they maybe go back to the GP. Missing school is a good enough reason for further medical investigation.
Just for a little balance our 7 yr old has been in hospital multiple times over the last 4 years with chest infections. No official diagnosis, although he is under consultant care. He has many weeks off school, but the school has always known why he has been off. I’m a little puzzled why the Head rang you, as they should have known the reasons for absence already.
Jnr FD doesn’t get colds, or illness, he is either 100% fit and healthy, or literally moments from death. We keep him away from kids that have colds etc (as much as you can…)
He has had multiple blood test which noted he was missing antibodies, which have now been boosted, but he still gets ill, just not as much.