I have that problem as well. I have one CD player in the house which will not look at CDs I have burnt. They'll play on any other, including the CD autochanger I have in the car.
From what I gather from my eldest son, who is an electronics graduate, this is common. Also, CD-Rs are much less prone to this problem than CD-RWs. The only problem with a CD-R is that once you've burnt it there's no going back. But at about 20 to 30p each, that's hardly a tragedy if you destroy the odd one.
The only thing I can think of is maybe some other software could be interfering with the cd players device drivers (is that possible Mark?)
I mean - you could have something running that prevents the cd player from working correctly, and when that something is switched off, the cd player could be fine again... but this is a total theory, and this is all a huge guess