Peter,
Odd. I've encountered a problem with a similar message on a Nokia 2690, which we tracked down to being a fundamental lack of support for HTTPS on the phone, and weren't able to resolve, but have never seen a 2700c demonstrate the same issue (especially if it worked previously).
It's possible that there are issues with the certificate authorities on the phone, although I'm not sure how their settings would have been changed. Have you tried to factory reset the phone and start from scratch?
Alternatively, I've seen such a message ("secure connection not available") simply mean that network connectivity was not good enough for the page to load, so it's possible that this issue was simply related to network congestion. Did you have any other phones you were performing installations with at the time?
-Clayton