Recently, Kenjiwing of Korgath brought this phenomenon to the attention of the official forums. There is currently no penalty for a team that fails to join an arena battle once the queue pops. The team that actually does show receives no reward and the match is recoded as a draw, which does not count toward the requisite games for the week. They are left to wait for another battle in hopes that the other team will show.
This process facilitates win-trading and avoidance of unpopular maps (OK, Blade's Edge Arena). Some addons will tell players which maps they were assigned before they enter. In a win trading situation it would not be difficult to have both teams check in with each other before accepting the invitation to battle.
Throvaldr of Akama insists that this mechanic should stay in place. He would prefer not to have to enter an arena when his partner has disconnected. Evulflea of Cho'gall countered that that is a risk we take playing an online game with a partner with a spotty connection. We've probably all disconnected at a particularly inauspicious time in the past.
The complete list of rules for the official 3v3 arena tournament have not yet been released. They may limit the number of queues a team can miss, place penalties on missing battles, or leave the existing system in place. While arena epics are pretty, they're really just polygons, but $75,000 is really a lot of money. While Blizzard hasn't spoken up officially yet, most responders agreed that the problem of queue dodging is a serious flaw in the game and should be addressed as an exploit.