Kshaya Masa is a special month in Hindu calendar and panchang. The calculation of it is based on tithi (the lunar day). A lunar month consists of, normally twenty-nine and half solar days. The month itself is divided into two halves called Shukla Paksha (bright fortnight) and Krishna Paksha (dark fortnight), beginning with the new moon and the full moon, respectively.
When a lunar month records no transition of the sun, it is called Adhika or Mala or Purshottam Masa and a lunar month is added to the calendar. On the other hand, when a lunar month records two solar transitions, that month is called Kshaya Masa and it is the expunged lunar month.
According to Siddhanta Shiromani, the Kshaya Masa occurs in the three months from the lunar month of Kartika, while the Adhika Masa is the remaining eight months starting from phalguna to Ashwin.
However, Kartika Masa can be an Adhika Masa or Kshaya Masa. Normally, the year which has a Kshaya Masa also has two Adhik Maas. But beyond the lunar month Magha, there cannot be a Kshaya Masa.
This kind of expunction or addition of a month in the Hindu almanac is in order to tally both the solar and lunar years. Since the Makar Sankranti (the transition of the sun to the sign Capricorn, which occurs on the fourteenth day of January as per solar Gregorian calendar) is the day of reconciling both the solar and lunar years, these kind of additions or expunctions cannot be done beyond the lunar month Magha in which this transition occurs.
It is due to this inbuilt correction procedure that season does not change their fixe time. Otherwise, we could have the festival of Holi, for example, falling in the rainy season! The Hindu calendar has this unique self-correcting method built into the system, which is normally not found in most of the lunar calendars adopted by other ancient civilizations.
Source -
Jyotisha Prashnottari (1995) Bhojraj Dwivedi - Diamond Publications New Delhi
Bharatiya Jyotisa Ka Ithihas (1974) Dr Gorakh Prasad - Hindi Samiti Lucknow
Encyclopedia of Hinduism Volume VI - page 146 - IHRF
As per calculations, Kshaya Masa occurs after 141 years or
19 years.
The last Kshaya Masa was in 1983 AD. The next will be in 2124 AD.
The sequence of five Kshaya masa are 1823, 1963, 1983, 2124, 2284...
Source -
Jyotisha Prashnottari (1995) Bhojraj Dwivedi - Diamond Publications New Delhi
Bharatiya Jyotisa Ka Ithihas (1974) Dr Gorakh Prasad - Hindi Samiti Lucknow
Encyclopedia of Hinduism Volume VI - page 146 - IHRF