How often should the headset be tightened?
To check your headset, sit on the bike, lock the front brakes, and push forward/backward with your feet. If you can see any looseness in the headset it needs to be tightened.

Since it's so easy to check one should check a few times a year. But no real "schedule" is needed.

I've seen headsets that were remarkably loose.  Though looseness affects handling to a degree, most people don't notice the problem until (in the old threaded headsets) it gets so loose the ball bearings fall out.  Then the bearing grinds and makes handling difficult.