You're gov salaries may be a bit low so those uni teachers go get jobs in corps where they earn more. Gov salaries should be no less than 75% of corporate salaries as a guide-line.
Up your edu priority for uni teachers by 1 or 2 (assuming you use a 120 total) and swap something for a couple of thousand of them to prevent closure of more unis. More unis closing will start a downward spiral as you train less uni teachers etc etc. The other enemy could possibly be a large drop in the amount of people of the right age to become uni teachers, check your education and pop pages. This last is unlikely for older people though and you would notice it among all sorts of workers.
Last thing, NEVER build schools, uni's etc if you dont have enough workers for them,