Sometimes (here in Texas where it never freezes the ground) the heads are actually set on "funny pipe" which is a short bit of flexible pipe that is then attached to the PVC pipe. If you dig up the entire head, you might find it attached to this softer black pipe, not white or grey hard PVC. If so, you can dig a bit deeper and reset the entire head a bit lower, or even a bit left or right if that will help protect it from the mower. The sprinkler heads I've seen are either the old fashioned 4" rotary heads that throw a long way, like 20'-30' or the smaller spray heads. In both cases there are concrete rings that can be bought from irrigation supply stores that will allow you to protect the heads from mowers.
That said, I have still managed to cut the head off of one and I insist that it was an accident, not anything deliberate done just to underscore that I'd requested that this head be lowered and my husband insisted that it was not necessary.
With the St Augustine grass that we have, if you don't weedwack around each head every week, after about 3 or 4 weeks the head can be totally lost. Once it is covered over, the head will try to pop up but it can't and so the O-ring gets cut out. Eventually the whole thing fails and water gushes or oozes there while the rest of the zone suffers low pressure. Dry grass is easy to spot but dry shrubs may die before you notice them. If you have the collar on it, you can eventually find it by hunting with a long screwdriver in the general vicinity where the head ought to be based on regular spacing. But hitting the head or the collar is still a hassle.