This morning, the HTC Wildfire refused to connect to wifi at work - kept saying "Scanning" after wifi was enabled. Reboots did not solve the issue. After I took it home too, it continued to refuse to connect. Many scary scenarios are described on the web, like having to do a factory reset. Anyway, turned on Airplane mode, turned off Airplane mode, and hey presto, wifi working again. In the evening after going back to work too, it connects without a hitch.
So, the solution was a simple Airplane mode toggle. Probably some hidden bug.