The various flu viruses mutate while it gestates. Before the host even realises he or she is ill, it's already slightly different than the previous host. It's one of the reasons the flu can't be annihilated like other viruses. I'm sure that the Enclave prepared for that, but life has a funny way of biting in the ass when it comes to artificially created creatures.
If the Flu killed all it infected it would have died out long ago. The Enclave Virus kills 100% and it kills fast. Its a super virus created by
"Science!" Without a host it can't survive. Once all the people are dead it will die.
As for the idea it could find another creature to live in. I find it unlikely. There arn't that many creatures left to start with.
"Science" can be used in this case to say it would just kill humans and human mutations then die out as intended. If you don't buy it, then
"Science" can be used to create a one shot inoculation. Some inoculations do get pasted down by the parents to their kids. Only every other generation or so may need to take the inoculation again.
Enclave scientests can test the remaining life and if they detect the virus they can use
"science" to get ride of it. I am sure the Enclave would test anything from the main land before they put it into their bodies.