I busk with my acoustic guitar once every one or two weeks. I have to play with medium strings so I can project and play louder, but as a consequence my left hand begins to hurt within two hours of playing. Eventually I can't hold down any chords, and I have to stop early . What are some ideas that I can use today to keep me playing for hours? Thanks!

tl;dr - Tips to instantly last longer playing acoustic guitar for 3+ hours
From the title of the post, I thought you had mistaken the UG forum with an ED forum. Can you play by yourself for 3 hours? If you can, how hard are you gripping(again fits with the ED forum) the neck? Try to use as little force as possible and relax.

Good luck with the stamina.
Yeah I made the title like that so people would click haha. Yeah I just finished and I tried pacing myself. I strum loud so I need to have a firm grip.
i dunno about you, but an inflate-a-date would probably be a better tool than your guitar. how you "busk" is your own business but i'm against the inhumane treatment of guitars( unless you have a Dean exotic wood series).
but if you really wanna last longer... just put an image of CaptainCranky riding a jackalope in your head !!!
need more gear and a lot more talent(courtesytuxs)
Go electric and use a small amp, like the little Danelectro Honeytone.

Or, just amp your acoustic.... A contact pickup is pretty cheap.
amp your acoustic, use lighter stringts or take breaks. most of the people i know who play till their hands (or wrists or arms or shoulders) hurt end up with long-term or even permanent issues. i've seen plenty of buskers playing an acoustic guitar through a small, good quality amp like a roland cube.
Quote by Skeet UK
I just looked in my Oxford English Dictionary and under "Acoustic Guitar", there was your Avatar and an email address!
I had that problem too. I play in jam sessions a lot and sometimes at church. But anyway I found that nickel strings help a lot, I've been using them for about a year or so. You lose a little bit of volume but not too bad. If you think you might like to try them I'd recommend thee John Pearse ones or the Martin Tony Rice sig strings(my new fav)