With a horizontal consensus like this (as opposed to a vertical chain of consensus, like a PoW chain) it is possible for the consensus to stall completely due to inability to reach an agreement. You've allowed a maximum of two rounds of consensus to occur, so what happens when both of these fail to reach an agreement? Why can't that happen?
The two rounds limit refers to the amount of time nodes accept transactions through broadcasting. So if node A tells node B about a transaction from the past (more than 2 rounds ago), node B will ignore it.
But the consensus part is different than the tx broadcasting and lasts for more rounds. Node B can specifically request some account information from node A, e.g. he's behind with the transaction chain for that account, and update its state accordingly.