Playing backing guitar can be VERY tiring. I played backing guitar for 4 or 5 years in a Scottish/Irish band and the gigs could sometimes stretch to 4-5 hours. This brings wear and tear both on your fretting hand (sometimes thick callouses could be virtually decimated in one night) and on the strumming arm. The main tiredness for me came with the latter as I tend to be quite "physical" in my backing and I did suffer bouts of tendonitis. You do tend to build up the necessary strength and stamina gradually but an intense 5 hour gig in a packed smokey venue WILL leave you wrecked for a couple of days however practised a fit you are.
All this got too much in the end on top of a demanding day job and I quit the band (there were other reasons too including lugging the PA on my own and doing aall the setting up and mixing but that's another story!). Now that I play more in the occasional session and more for "myself" and backing singers, I am enjoying my music much more again which is the key thing for me.
I would suggest, as others have done, working up your technique and stamina gradually, taking breaks where you can and varying your technique to avoid injury to ligaments and tendons, etc.
Good luck and best regards,