Everyone gets the same picture
The date is the only ingredient. Your browser turns today's date into a number and that number picks the grid, so two people on opposite sides of the world open this page and find the same puzzle without anything being fetched or compared.
The days before today are on a calendar under the grid, and each one still opens the picture that date chose. Only the day you were here counts towards a run, so a day worked back through is a picture, not a day recovered.
If you finish after midnight
A board belongs to the day you opened it. Open one at 23:59, finish it at 00:05, and it is filed under the day before, which is the day you actually solved.
So a late night does not quietly cost you a day, and it does not tick off tomorrow either. The next picture is still there waiting when you come back.
What keeps a run going
One solved day adds one to the count. Solving the same day's picture a second time adds nothing. Skip a day entirely and the count starts again at one when you next finish a puzzle.
There is no way to buy a missed day back and none is planned. A run you can repair is not really telling you anything.