So yeah... you can go forever, pretty much (Destiny)
Just finished up a pretty ridiculous run at the Verdant Forest. We were all randoms, and nobody was using the team chat, so we weren't communicating... but we pretty much agreed to give up after 122 rounds. (I took a screenshot near the end - I thought it was AT the end, but it was only round 119.) We killed our last 2 minutes by dancing with each other, then went in and killed the bosses.
It took 90 minutes. We had about 20 deaths, total (spread between the three of us). We killed a couple of thousand baddies.
We could easily have kept going - we got down to about a minute around round 115 because one of the guys wanted to quit after 110, but the other two of us kept going. We spent a lot of time dancing to convince him to play some more, otherwise we'd have stayed above 4 minutes, where we were for most of the run. (5 minutes is max; you can't get past that. We were on a plate at 4:58 once, and when the 20 seconds were added, we jumped up to 5:00.) He came back, played with us for a few more rounds (the screenshot shows 1:08 on round 119, but we were at 2:13 when we stopped killing stuff on 122), joined us for the boss fight.
I'm not sure what the point would be (of keeping going), though. You can't even immortalize it, except by taking a screenshot; none of the online stat apps (including Bungie's own game viewer) keeps track of number of clears. (Maybe someday there'll be an emblem or something?)
It was fun, but I don't really want to do it again. ;)