4 of these nodes suddenly loose communication from the other 11, but can communicate between themselves. These 4 nodes will likely get "stuck" immediately. They are not able to achieve a majority regarding any pending committals as they are not able to receive the votes from the other 11 voters.
Even in the case where there are no committals pending, the split of 4 will be aware that something is amiss upon one of them presenting a new transaction, as the set of nodes those 4 expects to acknowledge the next transaction, 11 will not respond.
And what happens when some edge case means that the 4 are not aware of their previous connections to the other 11?
This kind of reactionary design is very fragile because it relies on state transitions. If you start from scratch with two groups, one of 5, one of 11 which operate independently (for whatever reason), forming separate valid consensuses but are supposed to be on the same network, what happens when they rejoin?
This IMO is a critical issue that proves block chains & POW are not truly Byzantine tolerant, because there isn't a majority agreement that can prevent changes to history. Bitcoin's use of POW results in an asynchronous network, as there is no mechanism to vote and thus prevent historical changes, and it has been proven that asyncronous networks can not tolerate even 1 Byzantine failure.
In Bitcoin's case the single Byzantine failure is when someone produces a Proof of Work that exceeds the one currently in place. In essence by presenting it, they are disagreeing with the rest of the network about what the state should be, and thus it can be classed as a Byzantine failure.
In POW the votes are the blocks. The chain with the most votes becomes the canonical chain. The reason for this choice is that it is very robust, simple and doesn't rely on any state transition, reactionary design and is resistant to sybil attack.
It has been argued that POW is ,in fact, *the only* solution to the byzantine generals problem:
https://gist.github.com/oleganza/8cc921e48f396515c6d6