How To Avoid Vocal Fatigue When Singing In A Loud Band?

There are a few things that could contribute to vocal fatigue:
Why not start with ‘blaming others’ before doubting one’s technique? 😉
And with that I mean everyone else in the band creating lots of powerful acoustic pressure waves e.g. in rehearsals or on stage….
The thing with the shape of the vocal tract is that sound waves can travel in both directions. Just like sound travels in and out of a cone of a gramophone / phonograph. In one, the movements of a needle are converted to air pressure waves in reproduction, in the other, air pressure waves are converted into needle movement when recording sounds. The cone enables both. [It matches impedances, low resistance at the wide opening and high resistance at the small opening. It doesn’t actually amplify, hence it works in both directions.]
So when someone else is creating thunderous air pressure waves whilst you are trying to sing a few steady notes, these ‘thunder waves’ are travelling down the vocal tract and interfere with the vibration pattern of the vocal folds, which you then have to compensate for. Obviously, this causes the muscles to fatigue faster. With lower notes, there may be more flexibility in the vocal system to tolerate external input better, but with high notes, where there is much less room for tolerances, outside input can more easily throw things off balance. (There’s a study on trombone player’s lip movements being affected by timpani players.)
Ironically, if you sing with a PA and everyone else turns their volume up to match yours, you’re effectively inviting everyone in the room, including you, to play bouncy castle on your vocal folds.
Best would be to sing in a separate room, where no noise apart from acoustic voice can be heard. Second best would be to ask everyone in the band to turn the volume down, so that you can sing without a PA… oops… or at least with PA/monitor speakers that aren’t pointing at your mouth… or with in-ears for everyone, and the drummer in a separate room.
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Fatigue also happens when muscles simply run out of fuel and/or there isn’t enough lubrication in place.
Fuel, make sure you eat well before rehearsals, and perhaps eat during rehearsals, eg sandwiches, bananas, carb gels, etc.
Lubrication, obviously drink plenty during the day and try coconut water during rehearsals (works for me, seems to be less drying than water when singing), is the room air conditioned/heated/dry (some people take hydrometers into singing spaces).
Also, the usual smoking/caffeine/alcohol can play a role in fatiguing, although some people are affected differently, see what works.
Sports and energy levels, I always find that training on the same day before singing seems to deplete energy levels for singing well. On important singing days, I don’t train, at least not before. Also, having only one meal between training and singing seems to never be enough.
Late nights also lower vocal stamina, regardless of hours slept.
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Finally, techniques that work for certain styles or tones eg the ‘healthy’ and ‘relaxed’ ‘open throat’, ‘letting go’ are not ideal for the upper sung range of males between let’s say Ab4 and Eb5. Those techniques are good for lower and mid range, but when aiming higher and for longer it becomes more about efficiency (On my track Drowning, I’m holding a connected, chest voice D5 for nearly 20 seconds.)
Generally speaking, a narrower setup of the vocal tract will help to raise resonant frequencies of the tract. For example, working with more twang could help in exploring narrowing in other places too.