No, you have to save it to keep it.
Personally I like to use a button on my stick to start the film recorder. This way I only film the action. Once I decide to go in, I flip on the film and when I'm back in the tower
I stop it and save it naming it with titles that help me find them like "dumb move against a spit16" and so on.
Others like to film the whole sortie.
Films are great to see how the fight progressed and are a great learning tool. If you can take it, you can post the film to the boards and ask for pointer. But beware, some of these guys can be pretty brutal.
Welcome to Aces High!