We already have the PQ(s) downloaded before activating Cache Register. It automatically picks up that (those) downloads when it finishes sync with the GPSr. Just hit the yellow SYNC bar and the installation begins. Done in seconds. No real need to have geocaching.com open at all, not even for the field notes upload. Field notes will be present next time you log in.
... is why I say that logging in is unnecessary.
The first time you ran Cache register, it asked you for your username and password. After that, it logged into geocaching.com automatically every time you ran it. It needs to do that in order to upload field notes to the right account. When you receive a message asking if you want to log into geocaching.com, it is referring to actually opening a browser in order to create new pocket queries or edit field notes, which, as you say, is not necessary.
@MillfordGeoM Are you logging into Geocaching.com web site through the facebook link or from the regular login? I don't think the facebook login will work with Cache Register. If that is not your problem, you might want to try posting on the Delorme forums, might find someone with a similar problem and possible solution there.
The Delorme forums seem to point to a Groundspeak issue There seem to be a few of us experiencing this problem, mostly the past 2 months or so it seems. It appears to happen when the password is changed.
I am not using the facebook link
Any other thoughts are welcomed