I've accepted a challenge and suddenly it appears as if I've abandoned it. 

That occurs when a challenge is related to a group. If you're in a group and that group has a private challenge that only members of that group can participate, your participation in that challenge will finish if you abandon that group. 

In this case is really important you never leave a group that has a related challenge, otherwise, even if you leave the group and enter again, you won't be able to join again in the challenge.