Is it possible to have mumps twice?

Yes but: It is very rare. There is only one serotype of the virus known to cause infection and if you were infected once typically you are thought to have lifelong immunity. There are case reports of persons having a second occurrence of mumps, but it is rare enough that there is no rate data for such an occurrence.

Mumps: Only if your mumps titer (the antibody level in the blood to the mumps virus) gets too low. If you are immunocompromised you could be at risk.