The other day I had a text exchange with a priest friend asking about why, because it is a leap year, we didn’t celebrate St. Matthias. He wasn’t sure about why the leap year changed the date.
I responded that it was that it was an Ember Day in Lent, so we observed it, but I explained something about the leap year. I’ll give you a nutshell version, leaving out all the stuff about the Julian and Gregorian Calendar reform.
It has to do with the ancient dating. Matthias was/is in the Vetus Ordo calendar on 24 February in today’s way of dating. However, on the Roman calendar, which is still listed in Novus Ordo books, it was/is slated for the vi a.d. Kal Martii (the 6th day before the Kalends of March). A leap year adds a day at the end of February but it doesn’t change the date of vi a.d. Kal Martii. Instead it adds an additional vi a.d. Kal Martii… a Second Sixth… Bisextilis. That means that there are TWO 6th days before the Kalends of March. The Vigil of Matthias would be on the 24th and the Feast on the 25th.
Poor Matthias can get bumped around in the Novus Ordo, too, since his Feast can coincide with Ascension Thursday.
St. Gabriel of the Sorrowful Virgin – celebrated on iii a.d. Kal. Martii – also moves because of leap year. He is, in the Novus Ordo, on 27 February (iii a.d. Kal.). In the Vetus Ordo, on regular years St. Gabriel is on the 27th (iii a.d. Kal.) but the addition of the “Second Sixth”, this year he is on 28th (iii a.d. Kal.)
In the 2005 Roman Martyrology, we find entries today, 29 February, for the Pope St. Hilarius (+468), St. Oswald, Bl. Anthony of Florence, and in China St. August Chapdelaine a priest of the Paris Mission Society, who was arrested with many neophytes, beaten with 300 blows, partially buried, and later beheaded.
BTW… here is an page from the amazing Smithfield Decretals (France – 14th c) which is known for its fantastic marginal drawings of battling rabbits, a medieval Yoda, and Reynard the Fox – certainly inspirations for the online game base on medieval manuscript figures in which figures such as St. Hildegard of Bingen duke it out with warring marginalia – I digress. On this page, about half way down the right side column is an explanation of the leap year and St. Matthias the Leap Saint.
A standard solar year has 365 days and six hours, so in four years’ time these hours make 24 extra hours, which must be added as a new day to every fourth year. This additional day is what we call “double-sixth-day”, because, although it is counted as an addition, it stands under the same number as the previous day in the calendar, so that the two days are regarded as one and the same. The extra day is inserted in the calendar after 24 February (six days before the first day of March) so that we celebrate the memory of St Matthias the Apostle (24 February) on the next day, too.

Other points.
Bisextilis is not a Jesuit feast day.
Ember Days were often the days for ordinations.
People born on leap days are called “leaplings”.
Most of the Apostles Feasts seem to be distributed through the year toward the end of the month.
Ash Wednesday has not yet fallen on a 29 February and it won’t until 2096.
Tidal friction in the system of your planet and its moon slows your planet’s rotation down so that a day is lengthened by some 1.4 milliseconds per century. In about 4 million years, we can stop with the bisextilis correction.