From what you have said the cause of the leak, a blocked drain, was reported within the first two years and eventually the problem was cleared. However, it is clear to me that the underlying root of the problem has not been sorted out.
It could be that the drain blocking is as a result of your neighbour putting things like nappies down the toilet. OR it could equally be because the drain is partially blocked by builder's debris, in which case the warranty should still cover it.
You do have to ask why your neighbour doesn't immediately mop up the overflowing water as soon as it happens as sort the problem. It is doubtful that your neighbour's contents insurance will cover you costs as it is the buildings insurance that would pay out for the claim. Your managing agent should be contacted about the blocked drain and making a claim.