You should be able to put a password on an arena challenge. Here's why:
People frequently use the arena to exchange friendly attacks with each other, whether it's to trade painless xp, or just to see who's better.
But there's nothing in the game stopping someone else from arena-jacking them and attacking them in the arena while they wait for each other.
Most players are against this. The fact that the term "arena-jacking" is more common than the practice is pretty good evidence of this--and it's also good evidence that people consider it similar to "merc-jacking" and "team-jacking."
Since AIW added passwords for not only mercs, but also Team Mission members, I think it would make sense to add them for arena challenges as well.
This would also be more in line with the Clan Arena, where some other clan can't come and steal a challenge meant for someone else (although the mechanism would be different).
To give credit where credit is due, this is Blood Count's idea, not mine; I just think it was a really good idea, and he hadn't posted it yet.