When Rotom changes into an appliance form, it learns a new move in the same way that other Pokémon may learn new moves upon evolving; if Rotom would change from one appliance form to another and knows the special move of its current form, the old special move is automatically forgotten and Rotom learns the new one. If Rotom changes to its base form, it forgets the special move of the form it was in (if it still knows it)
Source
Rotom or Rotom-Frost can only learn Blizzard through changing it's form; TMs and Move Reminders don't work. And cases like your's have happened before, it seems to just be a feature of BDSP.
Unfortunately, there are only two ways to teach your Rotom Blizzard. One is by catching the Rotom in the Old Chateau (post-E4), and using the Secret Key in the Team Galactic HQ to access the appliance room. The other, if that option isn't available, is by trading it to a different BDSP game where it is available, and then trading it back. Your Rotom won't lose Blizzard upon trade, only after being placed in HOME.
Hope this helps!