There's no event quest available on my character - is there a limit to the number of times this quest can be done? I haven't done it at all on this character.
There isn’t. Only thing I can say is to check the “complete” section of your quest tab and see if you’ve done any and the date it was done. I asked if you’ve done it on other characters since I know if you didn’t download the new setup after the patch, you don’t see the quest on any character.