It may be just a case of the vent itself leaking and the cover just makes it hard to seal the vent properly. The vent is basically a 14 x 14 hole in your roof and if it is not sealed properly to begin with, the cover will not stop the leak.
I have two vents with Maxx Air covers that I keep open at all times in Florida with heavy rains. I have never had any leaks from them no matter how hard it has rained.
Take off the vent cover and seal the roof vent properly and I think it will solve your problem. After the leak is fixed, put the cover back on and you should be able to leave your vent open whenever you want.