Just to say an attendence of 85% is really low! It's nearly a day off a week.
We can't even blame the statistics - it's not that he had one week off in the 1st half term so one week in 6 weeks ( would give aporox that percentage ). He's not a little kid getting chicken pox and ear infections, he's a 13yr old enough has had a bit of a tummy bug, a few colds and bumped his head. Of course it's possible to get a significant head injury falling over in a corridor but really it's pretty unlikely (or did he run full tilt into a wall?) .
Op I can understand the schools frustration with you as well as your side as a working parent. I assume this isn't the first time they've aporoached you about it.
Barring the usual mumsnet " no special needs, no bullying " caveats he needs to man up and go to school! Ok maybe a couple of days off for the gastroenteritis but a cold " and he slept all day" - wouldn't we all given the chance, but actually we learn to get on with it.
You are enabling him in behaviour that is compromising his education and will make him, long term unemployable - what employer would keep someone with an 85% attendence record and no significant medical issues? Odd sick days of the pattern he has would very quickly bring you into disciplinary procedures.
Just for comparison my 3 were almost never off school. Dd2 had maybe 3 days last year in total - not a month or a term, in total. DS had a few weeks off ( in while school carreer) pneumonia, and rugby injuries ( neck, torn muscle and fractured clavicle - and the memorable hockey ball to mouth ,where he couldnt eat/ drink ! ) . I'm sure other kids of mn are similar. I know kids with chronic diseases (diabetes , asthma that needs steroids or admissions) who have better attendance records than that.
So as I say I'm very sympathetic to the issues of a working parent trying to get time off etc but actually the problem isn't school, it's your parenting of your son as regards appropriate behaviour when poorly. Hope you can get him on board and in school.