I thought it was tipple, i.e. knock it back= drink too much, and also fall. But on reflection, it's probably topple, as tipple doesn't seem to be a verb in the latter sense, according to Chambers anyway.
I think 'knock it back' rather than 'knock back' points towards tipple, but can anyone provide a dictionary reference to the meaning 'fall'? Otherwise 'topple', unsatisfactory though it is, will have to be the answer.