The Christian calendar is unhelpful, indeed unreliable for several reasons, compared to the panchaangams, to help you in deciding when to do your father's annual shraaddham. This includes number of days in the month, lack of information when full moons and new moons occur, when eclipses of sun and of moon occur, times when inauspicious periods such as Raahu-kaalam and Yama-khandam occur each day, and transition of planets, to mention a few. Moreover, the dates when the Christian months begin and end do not coincide with those of the Hindu months.
So, you might wish first of all to consult a panchaangam and find out the correct month, e.g. chiththirai, vaikaashi, aani, aadi, aavani, purattaashi, aippasi, kaarthigai, maargazhi, thai, maasi. Also, in addition to knowing the thithi is dvaadashi, whether it falls during the "valar pirai" (shukla paksham), or "thei pirai" (krishna paksham). The former is the 14 days after new moon when the satellite waxes from new moon to full moon, and the latter is the 14 days when he satellite wanes from full moon to new moon.
In other words, your father's thithi dvaadashi can occur in the val;ar pirai or tghe tghei pirai of one of the mlntghs named. Once you have ascertained this, i.e. maasam, pirai, and thithi, the shraaddham can be held annually accordingly without misgivings.
Incidentally, the thithi does NOT fall on the same date each Hindu year (any more than it does each Christian year).
S Narayanaswamy Iyer