Given this protocol, can you find some weakness?
One weakness with this protocol is that the compromise of a past symmetric key, which can often be assumed over some sufficiently large period of time, compromises all keys and messages sent after the time that key was first used. 

edit:

If any $K_{ab}$ is compromised, a man in the middle attacker can resend message 4 corresponding to the compromised $K_{ab}$ and it will be accepted by $A$. The attacker can then impersonate $B$ communicating using the compromised key.