I can confirm that it is very tricky when the BP doesn't print at the original point of departure. Telephone check-in will be cancelled at -30 unless they see you as physically checked in with a BP having been printed. The agent handling the connection will not know you are coming unless she digs further into your reservation to see you have boarded your 1st flight (which I don't think any of them do), and assume you are a tel-checkin late- or no-show. You will have no short-con assistance (unless they are already picking up somebody else going to the same place by chance), and miss your flight if you don't get there before boarding is closed. And you will miss it even if you do get there in time, but the flight is full and your seat has been reassigned to somebody else. In which case you should be eligible for DBC.

I was furious last time I tel-checked in from ZRH. I got both BPs in ZRH without a problem. But no shortcon bus was waiting for my last-flight-of-the-day connection to Budapest. I ran it. And I ran fast. The agent in MUC had NO clue that I was coming, she had cancelled me at -30. And she was extremely confused to see I had a boarding pass. "Where did you get that? How? Impossible!"

The last bus had left, and boarding was completed with the aircraft having a later slot, still being at the gate. I think the cabin door was already closed, but I am not sure.
I showed my SEN card, and confidently expressed my believe in her capabilities to get me on the plane, saving us both from a ton of trouble. My charme worked (I was boiling inside but kept my cool), and she radioed the ramp agent explaining she had a SEN with a BP that she had cancelled me being only a phone check-in. It seems he checked with the pilot, who OKed it, and they magically made a small Lufthansa car appear and drive me to the plane. I think it was another ramp agent that drove me. Of course, it helped that I didn't have any luggage.

LH must clearly do something to prevent this situation. It is something about ZRH (and it seems some LH outstations) not being able to print onward BPs, or the onward BPs not showing as printed, and telephone check-in not helping if you get to the transfer airport counter later than 30 mins before departure.

Can anybody call some knowledgable person to check what we as SENs can do to prevent this in the future? Should we ask the SEN line to telex the gate? Should we ask the first departure airport to annotate the record? (This wouldn't help as the gate agent at the transfer airport would not look at the record anyway, just at the list of check-in pax, before she cancels anybody or orders transfer buses.)

I will constantly have this problem from TLL, where they can never print onward BPs. And from ZRH, where LX tel-checkin doesn't see the full seatmap of LH flights ex MUC or FRA.