The power of Twitter
I returned to my computer this afternoon and noticed Google Wave saying "you're offline - connect now" - which I couldn't as clicking the button did nothing. What I did next is likely to become my natural next step in situations like this - I searched Twitter for "Google Wave Offline" and it seems the problem is widespread. Mystery solved.
This is the "real time web" in action - and as has often been noted this is a very significant development. The new web is mobile, people-powered and instant.