My LP copy develops a fret buzz after playing for 20-30 min.
It seems to be on all strings, but is more pronounced on the bass strings. It happens when I fret the 1st to the 5th or 6th frets.
If I set the guitar aside for a while (like 10 min or more) the buzz goes away, but then comes bach after I play for a while again.
I tried loosening the truss rod a bit, and discovered that it's already about as loose as it can be without removing the adjustment nut entirely (no, I didn't do that!)
The action isn't overly low, as far as I can tell (I haven't played many other guitars enough to easily compare/know the difference).
My guess is that the neck warms up enough where my left hand is, that the neck moves back a bit, causing the strings to lower a bit. My gut reaction is to attempt to shim the neck a bit.
Or pehaps raise the bridge, although it already seems fairly high above the body of the guitar. I expect that if there is too much thread showing that the bridge might get unstable.
Before I do something drastic, anyone have any ideas?
I wrapped a newspaper ’round my head
So I looked like I was deep
I would think about raising the action very little. I very seldom adjust necks unless all else fails.
Joe
I played tonight until the buzzing started, then I turned the bridge adjusters about 1/3 of a turn up on both sides of the bridge, re-tuned and played for another 30-40 min with no more problems. 
It makes sense that any adjustment I could make without dis-assembling the guitar would be the best thing to try first.
I wrapped a newspaper ’round my head
So I looked like I was deep
Yes thats true. Good to hear things worked out.
joe
