I think it must have to do with the fact that an incident photon with a sufficiently high energy will ionize the hydrogen atom (i.e. the electron will be ejected). Therefore it won't show in the emission spectrum. Is this correct?
The closest an e- can get to nucleus is the 1st, it can't get closer and so can't get to lower E. If an e- is beyond the influence of the nucleus and falls to 1s it can't fall any further (drop in E any more ). This represents the largest E emission. Once an e- is beyond the influence of the nucleus it doesn't matter how much further it goes it is still beyond its influence and hence the energy of the transition doesn't increase