Cannot check for purchases,

I've been having problems since about 8pm this evening with iTunes. I've been buying stuff from the store, checking for available downloads, trying to check for purchases... and I keep getting this message, despite the fact that I have no problems accessing the rest of the Internet (inc. this site), and two different speedtest sites report 39Mbps download and 8Mbps upload.

Is there some local fix, or could the iTunes servers possibly be under heavy load, what with the iTunes Radio having recently been enabled?