Thanks for the responses and confirmation that it can't be done.
Before this, I didn't know about Amadeus/SABRE and so that information is particularly useful (a mod changed the thread title and added the bit about Amadeus). I hadn't even appreciated there were different systems.
snczzz - you're right that I may not access anymore useful information by looking at checkmytrip.com. However (and I appreciate it's a minor point), I store all my upcoming flights on an iPhone app which uses checkmytrip.com to get the flight information so it's more of a convenience thing for me.