Getting knocked out (full HP depleted/falling into a "kill-zone") could still be an immediate round end, but (in addition to that) perhaps there could be a secondary win condition connected to a round time limit and, if that time expires, the player with the most remaining HP would win that round.
(This may, theoretically, allow as a win condition the possibility of getting one disc hit against your opponent and then turtling/evading/flying/clipping out of the map and sitting there until the round timer is up, but at least the rounds would have a set end point and someone who is able to do that effectively may not have incentive to continue doing so for very long since it might not be sustainably fun and other people are probably less likely to continue playing with them much if they don't find that fun. However, adding a round loss timer if you're out of bounds for too long might be useful to alleviate that part.)
I personally think 5 minutes makes sense for a hard cut-off, but...
...what are your thoughts?
Edit:
Perhaps the timer could be up on the wall behind on each side of the fighting arena and be an analog styled "physical" object in the style of other mechanical objects in RUMBLE? Perhaps it could start audibly ticking as the round timer is almost out and then a "round over" sound could play when the round finishes this way.