When this kind of question comes up on Dave's show, I seem to recall him saying to maintain a separate emergency fund for the rental business than for your personal life. However, I can't remember exactly what I've heard him say so I may be mistaken.
What I do, however, is exactly that (thus why I think I may have heard Dave say it
With more properties, we personally feel comfortable basing our goal amount on 50% occupancy - mainly because since we are in duplexes, 50% occupancy is enough to cover the mortgages across the board.
Ultimately I think it boils down to a question of how much risk you're comfortable with. If you're Dave - then that's 0 - Dave being extremely risk averse when it comes to debt.