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.