Quite often Adelphia gives "preview weeks" of digital channels in which anyone with their STBs can get those channels for a week or so. At the start and end of the week, I find the box automatically changed to Channel 1, the Adelphia information service channel. I am assuming that means that they reset the box to give and block the channels. If I unplug my cable from the box the day before the end of the preview week and plug it back in the day after, will I avoid some sort of "reset signal" and be able to retain the channels?

No. Cable box IDs and their assigned programming tiers are continually refreshed - it may take a day or two, but you'll end up with only what you're supposed to have. And if your cable company doesn't hear back from your box ID after a while (ie. you install a filter that blocks communications), the tiers on your box will eventually expire and/or your box ID will show up on an errata report as MIA and someone from the cable company will check out why they haven't heard from it.

Ok, thanks. Out of curiosity, why is it that the box always reverts to channel 1 at the start and end of these weeks?

Cable boxes usually revert to a "home" channel after a reboot. It is in the code, kind of like windows always boots to your desktop.

And some brands can be set to default to a particular channel every time they're turned on.

Yes, but this box does not convert to this channel every couple of days...only at the beginning and end of these weeks. It will turn on to the last channel that was on otherwise. Just curious...

Like Jim says, probably just part of a reboot or the result of a tier refresh.