The Proof of Stake problem lies in the fact that it pays to mine a number of alternative branches simultaneously. You can do this for free, with non-zero chance of success, i.e. increase the expected return. Proof of Work does not allow such tricks, so you only mine in one branch (you choose it). As a result, a consensus is achieved at some point in proof-of-work model, while it is impossible to guarantee convergence for pure Proof of Stake.