correct me if I am wrong, but the only time the server knows you are going to fail a puzzle is 24 hours after you start it. So you could factor in 24 hours to the average time for all of the fails.
if you don't solve a puzzle, you can click on the "recent games" link at the top and get back to it within 24 hours. I know that I have had my computer lock up in the middle of a puzzle and then went back and finished it after a reboot. I have also gotten stumped, worked another puzzle, then went back to the first one to try again.
Also, you cannot get 100% if they fail on the 24th of the month like you suggest. As soon as you start a game, that game counts towards your attempts. only after you successfully complete it does it count towards your solved total. If you start a game, then look at your stats while you are working it, you will see you have something less that 100%.