I view the signal as displaced energy from wherever the person has been phased to, quantum entangled with the phased matter so that it contains the 'pattern' to rephase the person back into our dimension. If the signal degrades, only part of that person can be phased back.
This nicely leaves open the question of whether the pattern has "resolution". Degradation could mean piecemeal loss of an infinitely sharp pattern...
The survival time of a pattern might be a feature rather than a bug, and related to the energies used in pushing the pattern into the "phased realm". Perhaps that realm involves energy loss, so that sooner or later the pattern will "drop back" to our realm - say, on the planet below. But if it's not sent to the planet below, it will drop back anyway, and that would happen either on the sending platform (which is why our heroes flicker on and off there when something goes wrong) or then deeper in the bowels of the machine (in which case permanent harm would be done to the pattern).
In this interpretation, "Lonely Among Us" would involve Picard leaving his physical self in the pattern buffer (where it would ultimately pop back from the phased realm and die) and using the carrier energies ("Energy only!") to beam out his alien entity self which was using its alien abilities to carry some of Picard's mind with it. The alien would know that sending an "empty beam" out there would serve its purposes, but our heroes would not immediately figure out what this weird misuse of their technology meant, hence they'd consider Picard lost forever. But Data insists his physical pattern still resides in the machine, which may refer to the phased matter stream that was never sent anywhere (and never mind the misguided writer intention that every beam-out involves leaving behind a reproducible physical pattern)...
Timo Saloniemi