D'you know what? It's now middle-2015 and the problem still persists throughout the Lumia range, as far as I can see on the net, and probably many other Windows 8 devices. MS haven't bothered to even make an attempt at fixing this.
And no, it isn't a simple matter of a corrupt security key: I had already set my wifi security to WPA-PSK+WPA2-PSK and, at any rate, I have wiped out the Lumia wifi connection settings and re-entered the key any number of times to no effect. This problem is always there: the connection will work for a few days until it decides to fail out of the blue. And you can't even try to fix it because MS don't give you a user interface where you can enter the various connection parameters, so that you can at least try to narrow down the cause of the software failure.
I've got so frustrated with this that I've thrown this piece of cr ... rubbish against the wall, a couple of times and, lo and behold, it started working again for a while. But I'm certainly not going to recommend this method on a public forum, just because it worked for me.
For me, the only solution has been to consign this piece of junk to the scrap heap and go back to an old Android smart-phone. Sure, there are a couple of apps, coded just for Windows phones, that I'll miss. But that's a small price to pay for the benefit of doing away with this frustration.