There is a technique that used to work on the OGs (Original Generation):
Learn the code the regular way.
Learn a second version of the code where you cover the emitter during the first half-second or so of the command; this learns only a repeating portion of the command.
String together one of the first part with several of the second part.

The problem I have heard about in this regard with the NGs is that they insert unrequested delays between macro steps. If the Panasonic is tolerant of those delays, this method might work.

The explanation for several commands in a row not working is that each command starts by telling the set that a NEW command is coming. That is why learning only the repeating part of the command could help.