When I practice guitar on my own at home or with my band, I can play for ~1.5 to 2 hours without getting really tired. When I am on a stage and we play a gig, I get really tired on the first half hour.
I can continue to go on, but I'm really tired. Especially my fingers and left hand(fretting hand). Why does this happen?
This may be wrong in your case, but given the evidence in the question, it's likely to be stress and adrenalin.
When you practice in a relaxed environment, you play in a relaxed style. You don't tense your muscles. You don't fret any harder than necessary.
With performance nerves, and the buzz of being on stage, you tense your arm, you fret more stridently, and that is more tiring.
I don't know whether you're an experienced stage performer - but if you're new to it, you'll find that after a few performances, stage nervousness becomes less of an issue.
As soon as you find your head is clear enough on stage, make sure you're mindful of a relaxed technique. Make sure that if you tense your muscles more than in practice, you notice it and put a stop to it.
Also ensure that your practice and performance postures are the same. Don't practice sitting down if you'll be performing standing up, for example.
And/or .. Dehydration ! This may not be the answer as it depends on your body, but something to pay attention to. ..
Do you sweat when performing, but not so much when practicing ? When you sweat you lose water (of course) and salt.
Half an hour is probably pretty quick for this to happen, but effects of dehydration and lack of salt are general feeling of fatigue, cramping/tiredness in muscles and sometimes you just think more slowly - kind of mental fatigue which can affect inventiveness and dexterity. I speak through experience !
So make sure you have enough salt (but don't overdo it!), and have a bottle/large glass of water avaiable. Sometimes after a couple of gulps, I can feel a difference immediately.
As regards to how much salt is "enough" : depends on your bod really. Try a packet of salted potato crisps or peanuts or something before you start.
Before reading slim's comprehensive answer, I'd have said the same. Last point, extended - when you play seated, which is like most folks do, your arm angles (fret and pluck) are PROBABLY quite different from those when you're standing. If you wear your guitar low, as seems to be the current fashion, your fretting arm in particular, will be lower to reach the guitar neck than when seated. This then changes the wrist angle and fingers have to work harder. Harder work = tired quicker. Practise in the same way as you'd perform - or wear your guitar higher so the angle doesn't change sitting/standing. Or perform sitting down !
