The following is my surmise, based on what I've seen. Perhaps the admin can clarify or confirm.
You can retry, even if the monthly competition has ended, but those puzzles will not count for the closed month. Once you hit the midnight EST time, no further completions will count for the old month. If you were in the middle of a puzzle at midnight, that is counted as a missed puzzle for the old month. That may seem unfair, but otherwise someone could open a bunch of browser windows and complete a bunch of puzzles after the "end" and perhaps end in a higher position in the rankings than they should.
Next question comes on how should those puzzles be counted for the next month. It is not really fair to show someone with over 100% even if they were charged with the open puzzle last month and credited for its completion this month. Again, you could have someone game the system, completing far fewer puzzles, but ending over 100% by spanning months and knocking someone out of first on accuracy who really deserved it.
No easy answers on how best to score the competition, but at least some attempt to be fair to all.