I have no idea what kind of server load there might be, don't know how one measures that. I've just moved my site to a new hosting company, and server response time in terms of page loads seems to be pretty quick. Don't know if that would be an indicator of server load necessarily.
I did discover one thing last night which might possibly be related to this issue. I hadn't been able to get my phpdig search page to work properly since the move. I'd enter a search term and click Go, but then I'd get the same page back. I went through my site to make sure there weren't any missing files of any kind, and after doing that, my search page worked properly. All this, too, when none of the files that I had to upload (or re-upload) was anything to do with phpdig searches.
Fixing all the little stuff that was wrong seems to also have fixed spidering from a secured web page, but I still had the spidering process just hang at a time of 9:53 into spidering around midnight last night. Go figure.
I guess I'll work with it a little more and see how it goes.