Yeah, by
killing the paladin. How the heck is that
cool?
Forcing monsters to kill downed PC's is
against the advice in the DMG. Without this houserule, however, is downright stupid not to do it.
Or, you know, move away from their bleeding body for a round and let it end when they fail to maintain the challenge.
My opinion on this is pretty simple: there's equally stupid arguments for it and against it. Most fighters can't do a thing against an opponent 6 squares away marked with a javelin throw, so them being on their feet or not is
clearly irrelevant to the marked condition (and even if one specifically can, not every fighter has options to do so, so it shouldn't be considered to be part of the mark). The mark is because the fighter is just that good at harrying opponents when they attack, preventing them from focusing on anyone else for a set amount of time (until end of the fighter's next turn).
So unconsciousness making a mark fall off is stupid for a fighter. It leaving a mark on is stupid for the swordmage (for some people, I don't have an issue with it, as it's magic). There's no net gain of changing the rule for the 'marked' condition, and no net loss. Therefor I prefer the option that keeps the rules as written unchanged.
If anything just change the swordmage mark to end when unconscious. Which is a change I'd dislike for power reasons, as the swordmage is the best single-target marker post divine power, no need to screw with this niche, but it's still preferable to screwing with the basic rules for no gain.
Edit: If the idea is to mimic the fact that the marker needs to be actively able to 'threaten' the target for the mark to work, then your proposed rule change don't really cover it... it should actually be marked conditions end when the marker is unable to make opportunity attacks, right? That models what you're going for more.