Yesterday I was talking to a mate who is learning the guitar, and I remembered to remind him to pull that axe in tight. It's something that you don't hear enough about often enough. In fact I think I spent the first 20 years playing without being told specifically; fortunately I was already doing it unbeknownst to me, so when I was told it made total sense.
Let me drill it into you for a moment, I consider it fundamental, and after this little read you can go away with an exercise to try and be informed up ready to pass on to other guitarists! ;)
...so why do you think it is the big burly fella struggle to grip out a bar chord for more than 30 seconds, and the little seven year old girl play them all day? It because most of the pressure you need to adequately fret a note should *not* come from your hand, it should come from your arm and shoulder.
Look at that wimpy little thumb muscle in front of you. Now look at that rippling biscep. Which one would you rather you were using to apply pressure?
Basically if you were to fret notes only using the clamping force of your hand, you won't have much playing stamina. If you pull the guitar in tight your left arm is the pulling force - your fingers are just forming the chord pattern - and your right arm is counterbalancing your left.
Not too sure what I'm talking about? Okay, here is the exercise. Form up a chord, whatever you want. Now, take your thumb off the back of the neck. What you'll find you need to do is what you should be doing - that is, pulling the guitar in and exerting all the fretting pressure with your arm. You should be able to fret without buzz, in fact play any tune you know, without touching the neck with your left thumb.
Of course the thumb is important to guide, help with dexterity/fine motor skills/accuracy, offer a bit of structural support/grip/pressure and occassionally fret a bass note - but it isn't where the majority of the force comes from. Playing a song without your thumb gives you an idea of where you should be applying pressure from, it's a bit of an eye opener if you've never tried it.
Good luck, and hopefully armed with this knowledge you will be able to play all day without getting fatigue in your thumb and fingers (if not at least pressure lines in your chest because you pressed the guitar so firmly into it!)