I went back to uni as a mature student, I have a pretty robust immune system usually when it comes to bugs but I was ill for pretty much permanently I'll for first 6 months. I wasn't off much but it culminated in an asthma attack and a pretty bad case of pharyngitis ('teachers cough') that just would not go for weeks! It made me cough so hard I was vomiting!
Plus this time of year there's tons of bugs about.
I also have friends who are teachers who experienced the same when they started their probationary years (especially those in reception classes where the little darlings just LOVE to wipe their nose on teachers sleeve, cough right in teachers face without covering mouth and haven't quite got the hang of hand washing after the loo yet 
)
Also stress and anxiety impair immune response so it could be a combination of the two! It can be a vicious cycle because also being physically ill can make you stressed/anxious.
He needs to go to GP get a full check up with focus on immunity, including vitamin and mineral deficiencies. Get good advice on supplements he can take and ways to boost his immune system. Low levels of certain vitamins & minerals also contribute to mh issues.
Does he smoke? Drink? Live on junk food? Exercise regularly? Drink enough in terms of hydration?
He could start eating more fruit, veg and whole grains, take vitamin & minerals supplements, probiotics (very good idea if he's had several courses of antibiotics). Do some light exercise.
The advantage of suggesting all this is you would be being proactive and supportive so if he's resistant then you can legitimately say 'are you serious about doing this?'
There is one aspect that's really worrying though, if he's not keeping up his attendance that could affect any funding he's getting and ultimately he could lose his place on the course altogether.