i don't think there is anything that eats exclusively termite queens, but one dies, from termite eating animals, other insects, or old age (they are still insects they only live a while, but since they breed up till the end many of their young out live them) but when they die, other potential reproductives (those that can become queens) develop into the reproductives.
In fact, this may be the best example of queen control (I may be confusing termites a other social insects, but I think this applies to most): The queens produce a chemical that keeps the potential reproductives from developing. When the queen dies then it stops producing that chemical, and the potential reproductive is no longer suppressed and develops into an active reproductive.
Also, some termite species may have more than one queen active at the same time.
I would recommend to everyone I know to take two courses in college: a basic ecology and evolution class, and a general entomology.
The former because it is fundamental to science
That latter because it beautifully examplies the former. And is actually pretty cool if done right