I don't know if a time frame is such a good idea.

Neither do I. These things don't work out according to time frames.

A time frame, or ultimatum, are probably better used when you've decided that you've done all you can, given it plenty of time and things have stayed status quo, and whatever happens at the end of that time frame or ultimatum is something you can live with happily. I think that's the criteria, rather than, for instance, you've run out of patience.