Ecrix tech support eventually got back to me on this one. They made two points:
i) Ejecting the tape is a good idea, and they strongly recommend it. They said that important file catalog information is written to the header of the tape when it is ejected, and without that header the drive won't know where files are on the tape. (This may be pertinent to what happened to you.) They suggest telling Retrospect to eject the tape when finished, which is what I have been doing.
ii) They didn't have strong opinions about the effect on the life of the drive leaving it on vs. turning it off, so long as it is well-ventilated and not in too warm a room.
They also said that they would write up the answers to my questions and post them in their FAQ and readme for the drive. I haven't checked to see if they've done so yet.
The backup machine, by the way, is a B&W G3 -- on-board Firewire, not a card.