The most recent Beeminder blog post contains a rant against mulligans, but I think it’s missing something really important. Though that blog post is not wrong in its complaints; it’s also entirely within the spirit of Beeminder to take a mulligan—so long as you are willing to pay for the privilege.
The problem is with free mulligans, not with mulligans in general. If you derail, well, that’s too bad, but you pick yourself up and try again after perhaps a short break. i.e. you get a mulligan! You didn’t fail, not in any permanent way; instead, you have a chance to try again.
Once upon a time Beeminder didn’t work this way: if you failed, you failed, no mulligans. If you wanted to keep at the goal you needed to restart it. That was, in retrospect, a terrible idea: it amounted to nudging people who derailed into giving up on their goals, the exact opposite of what they should be doing—taking the mulligan and starting over.
When you derail, consider the money you pay the fee you’re paying for the mulligan: you don’t get away scot-free, but you do get another bite at the apple, another chance to succeed at your goal. Derailing Is Not Failing—rather it’s a fee paid for continued awesomeness.