Translation:Please sing, because your sister is still singing!
I'm curious if you could use "... via fratino kantadas" or something like that.
Yes, that's possible.
[If I have the wrong suffix, I meant the one which means "to continue to".]
-ad- is probably indeed the suffix you're looking for, though it doesn't exactly mean "to continue to". It does put focus on the duration an action is (often continuously) performed.