macbook air won't connect to network

In the last two days we're having extreme problems getting our Macs to connect to a network. We have a MacBook Pro 2013 and a MacBook Air 2012 both running Mavericks. The network shows as available and moving closer to the router doesn't help. Other devices which are unaffected include FreeSat box, Windows laptop, various phones and tablets. Router 1 is a Livebox from Orange France, router 2 is a BT home hub 4.

In order of events:-

1. We were at our 2nd home, network had been absolutely fine all week, went to go online and no connection. Restarted router to no effect, discovered all devices other than Macs were fine. Eventually discovered that turning wifi off and then on again solved the problem.

2. Returned to main home next day, no problems connecting to network.

3. Tried to go online first thing the next morning and neither Mac would connect though all other devices are again fine. MacBook Pro eventually joined after being shut down and then started up again but lost the connection after sleeping then found it again after another shut down and start up.

4. MacBook Air will not connect at all. We've restarted the router, restarted the computer, turned wifi on and off again, removed networks and passwords and tried rejoining, run diagnostics countless times and basically tried just about everything suggested on this or any other forum to no effect. So far as we can detect, there have been no system updates or similar which might explain the issue and since the two routers are completely different it would be an enormous coincindence if both providers have done something to cause problems only with Macs.

I'm dreading the next time the MacBook Pro sleeps/has to be shut down as I think it's a foregone conclusion that it will lose the connection again and we won't be able to persuade it to connect.