This is my assumption only.
I think that the reason is that the specials are not needed. Whatever trains that are available as of now would be sufficient. One additional train to Patna or Varanasi is required. They do some specials to Ajmer during the URS. They do some specials to Allahabad during the Kumbh. But they are all intended for the people living in SCR zone.
Pooja specials & Diwali, Holi specials from north India to SC have to be run by the respective zones, if they believe that there...
more... would be good patronage for the specials. Ex: Santragachi to Mumbai, Chennai pooja Specials are being run by SER. Not by SR or WR. So they arrange the train for bringing in people home, instead of the the Mumbai, Chennai arranging the people to send home for their special occasions.
Speaking about the long holiday seasons, Dasara, Sankranthi & Summer are the main long holiday seasons. Diwali usually would get only one holiday for Govt. & Private organizations. Schools get 2. So people who would want to travel with their families on Diwali, they have to let their children bunk schools for atleast a week, immediately after Dussera....