Is there a LED flashing on the control board? There should be an LED that will flash with a failure code.
The blower motor is on a electronic timer, also, there is a high limit snap disc. I would assume the high limit is weak and tripping early, or the timer is bad and timing out longer than it should. Hard to say which, but I suspect the limit. The timer is electronic and I doubt it would sort of fail, it would just die. Another problem could be a partially clogged flue pipe causing the heater to run hot.
I would verify the flue is in good condition, and if you don't find anything toss a high limit in it. The limit is only a few dollars.
