Why do tithis sometimes repeat or vanish?

Each tithi lasts as long as it takes the Moon to pull another 12 degrees ahead of the Sun. Thirty of them make the full 360-degree circuit from one new moon to the next, in about 29.5 days. So on average a tithi lasts a bit less than a solar day.

But the Moon's orbit isn't a perfect circle. It speeds up as it comes closer to the Earth and slows down as it moves away, so the same 12 degrees can take quite different amounts of time. Running our calendar engine across thirty years, from 2000 to 2030, the shortest tithi came to just over 20 hours and the longest to nearly 27.

Your day needs one name, and the convention is to use whichever tithi is in force at sunrise. Now there are two possibilities. A tithi of 26 hours can begin just before one sunrise and still be running at the next, so it names two days in a row. A tithi of 21 hours can begin after one sunrise and end before the next, so no day carries its name, even though the tithi really did happen.

Sunrise depends on where you are, which means this depends on where you are too. A tithi that gets skipped in Delhi may not be skipped in Chennai, and that's fine: nobody has made a mistake.

If festivals simply followed the sunrise label, a skipped tithi could leave one without a day at all. They don't. Each festival rule asks for its tithi at a particular part of the day: Diwali needs Amavasya in the evening, Rama Navami needs Navami at midday. So a festival can land on a day whose printed tithi at sunrise is a different one altogether. Traditional panchang users also treat skipped and repeated tithis as less favourable for fixing weddings and such; that's a convention of practice, not something the astronomy says.