I have done non-Schengen to non-Schengen transfer at FRA following an evening arrival several times and never missed a flight. 'Usually' there are people to assist the short transfer passengers and once we were taken from the incoming plane direct to the outbound plane by bus. I have heard of one story where Lufthansa failed to look after a goodly number of people all transferring from one flight to another following a delay in arrival, but most often the case is far better than that.