AFAICT the only way to become immune to the cold and flu is to wear something with high environmental protection on your mouth, like a gas mask, all the time. You have a chance, based on your health score, to get sick every half hour, and if it happens then wearing protective gear can block it. No matter how high your health is, you still have a chance to get sick, and at realistically achievable levels of health you don’t make all that much difference. (At standard starting health of 0, with nothing over your mouth, I think you’ll average one sickness every 18 days, although obviously it could be much more or less frequent in practice, and at 100 health, which you might reach eventually if you take two vitamins and then one every couple of hours, you push the average to about 20. The maximum possible health is 200, but you would have to be eating a LOT of vitamins, because health slowly moves up and down with influence from the difference between your health and your healthmod, which is what vitamins affect, and healthmod trends relentlessly toward zero.)
Based on responses I’ve received before, I believe this is working as intended. Stock up on DayQuil! (Er… I guess it’s “non-drowsy cough syrup” now.) It’ll keep you functional while you wait for the cold to run its course.