IS it naive to suggest that its the obvious one? the phrase is asking why someone is silent, ie not using their tongue. Possibly something has stolen it, and if you've ever owned a cat their kleptomaniac tendencies are well known. OK, it's a simplistic answer, but I think this is one case where the cat may be a cat....
The expression "cat got your Tongue" comes from the English sailing ship days, and refers to the cat of nine tails, if the captain or other officer told someone something in secrecy he would 'get the cat' if he was to tell the others, naturally if the others wanted to know what had been said they would ask, tell us, or are you afraid!!! ..I.e. has the cat got your tongue!