By the way, the external HD involved in my particular problem is a G-Tech Mini 500GB 7200 rpm, and I'm using it with Time Machine which the HD seems to be working very nicely with.
Anyway, I actually did an SMC reset at the suggestion of an Apple online tech, but it didn't solve the problem. Today I tried another Apple tech who suggested I do a full system check (using the applications disk that came with my MBP), and the check eventually found a hardware error 4SNS/1/40000000:TmOP-62.250 (whatever that means!).
The system check took quite awhile, and I had to phone back later to talk with someone about it. The next tech couldn't find any reference to an error by that "name", and he suggested I visit the Genius Bar at my local Apple Store.
I did so, and my assigned Genius plugged an Ethernet cable into my MBP to do some diagnostic work. He found that everything, including the Firewire port, was okay. He reckoned the problem is being caused by power sometimes being shut off at the Firewire port (and I suppose other ports as well) when I put my MBP to sleep when on battery power and, of course, when I wake it up I get the "disk not ejected properly" warning.
Thing is, though, I don't have the problem every time I wake it up from sleep when on battery power, so that's a bit of a mystery.
Anyway, the Genius suggested that I not worry about the problem, not be concerned about any files on my G-Tech Mini being lost or corrupted, and basically ignore the ejection warning when it appears. Well, that's easy for him to say! 🙂
I'd really rather have the problem solved so I can then sail on as serenely as I used to with my previous MBP and its companion G-Tech Mini 250GB which gave me no trouble at all (interestingly, though, when I tried using the 250GB on my new MBP, I got the same ejection problem).
The Apple tech who suggested that I do a system test also suggested that I send a note about the situation to Apple.com/feedback. She claimed that Apple pays close attention to that source of feedback, so maybe we'll get more attention to our problem. But many of you folks no doubt have a lot more experience of dealing with Apple, so maybe you can enlighten me about the possibilities here. 🙂