The Login method sets the principal for current request only. Just after the request completes, the principal context is wiped out so that the server can handle other requests for other users. When a new request comes, eons later from the server perspective, the principal context no longer exists and if nothing restores it, the request is unauthenticated.
To fix this you have to return something from your login method to the client. Not only bool but rather - an authentication token. Something the client could use to authenticate further requests.
It could be anything. Forms cookie would be fine as long as the client remembers to append it to further requests. Another common practice is to have a custom authentication token returned to the client and then appended by the client in a custom authentication header. And as forms cookies are handled by the Forms Authentication module, custom headers would need a custom mvc authentication filter or custom asp.net authentication module so that the token is readed, the identity is extracted and restored just before the request is about to execute.
If you don't like to bake your own token infrastructure, I would also recommend OAuth2 tokens. There is a great book that contains easy to follow examples on this and other possible authentication methods: