Since last week, our server had been experiencing increasing instability.
Our hosting provider mis-diagnosed the problem, and decided to simply pull the plug on our server.
E-mailing and phoning did not help, so eventually the only practical way we could fix the issue was by switching hosting provider.
Looks like we were long overdue switching: our web site feels a lot snappier than before, so in the end it is probably a Good Thing we switched. Half the price, double the speed, it looks like! Yay!
Our apologies for the inconvenience and the flaky server! Hopefully things are sorted now!