They DO span endlessly, unless you meet the "defeat" conditions, which appear to be some sort of time-limit. I ran into this issue myself. All of my characters, with the exception of Gladys, died, so I just ran her round and round the center fountain, killing a guard when I could and healing my wounds/re-upping my magic shield between. I counted nearly thirty dead guards before I loaded a prior save and moved on with a different part of the game.
Returning to the quest at a later point in time, the quest was updated (you will receive a notification) after I managed to kill less than fifteen guards all at once. I surmise, then, that ALL of the guards must be killed within a set amount of time or more will continue to spawn. This theory is lent further credence by the fact that I often had the number of guards down to one when fighting with Gladys alone, however, new troops always spawned before it was slain.
You can also watch an online video at myGamers which shows how they continue spawning, up until the player has defeated all of the onscreen enemies at roughly the same time:
http://mygamersvideos.onlinewelten.com/videos/rFHC8Tnry7xM/
To summarize: kill them all and kill them quickly or you will face a never-ending horde.
EDIT:
I forgot to mention, do not bother searching for a key to the locked gate in hopes of avoiding the fight by moving on. I made that mistake as well (when fighting with Gladys alone). The locked gate will open once all of the guards are dead.