When doing the challenges a message pops up saying we have 60 seconds to complete the challenge. However, we all wait and enter at the same time (all three groups healer, tank and dps) however, about 15-20 seconds goes by and we get a message saying we failed.
Getting back to the OP's original question, it should give you a message when a team fails, something to the effect of "your healers are incompetent..." So you should be able to pinpoint the problem.
Our team takes about 5-10 seconds to assemble outside the gates, then we go in together (use your speed abilities). Especially the healers. You really shouldn't be failing due to expiration unless you're taking an inordinate amount of time to assemble.