Airport Express not visible to OS X (iOS is fine, though)

Question

I'm having fairly bizarre trouble with my home networking set-up. Specifically, the WLAN provided by an Airport Express base station. The whole set-up has been working flawlessly for some years, and on the network side, nothing has been altered recently (or anytime since the initial set-up, actually). However, the WLAN has become almost unusable by the OS X machines in the household. And *only* by these.
The situation is *very* strange insofar as from time to time, the two OS X machines in the household (one MB Pro, one MB Pro Retina) simply stop being able to see the base station, and the network provided by it. If that happens (and it has been happening more and more often recently), the only way to get it back is to power cycle the Airport brick. Once one of the two OS X machines "sees" the WLAN again, the other one is also able to use it. And if the problem occurs, both of them lose connection at the same time. It also might take quite a number of power cycles before the OS X machines "see" the WLAN again. Sometimes a single power cycle does the trick, sometimes it takes 20.
Right. Sounds like a dead, or dying, Airport Extreme brick, you say?
Trouble is, the iOS devices in the household (one iPad, one iPod, one iPhone) are always able to see the WLAN, and use the network. Concurrently. No interruption in service. The network speed is always o.k., and there is no glitch in communication. Even when the OS X machines are out of it.
However, there *is* something going on with the Airport Extreme, otherwise the two totally unrelated OS X machines, with no shared user accounts, different users, different data, different build date by about 1 year (2011 and 2012), different machine type (MB Pro, MB Pro Retina), would not both lose their connections at the same time once "it" (whatever it is) happens to the Airport. This has also persisted over the last few OS X releases, and just gotten more and more frequent.
I've tried the following:
Deleting all mention of the network from the OS X machines (passwords in the keychain, network config, etc). No effect.
Factory reset of the Airport Extreme brick. No effect. The OS X machines have exactly the same trouble "seeing" the reset brick with its default "Apple eaXXXX" network as they had with the configured network. It also takes a random number of power cycles before I can use the utility on an OS X machine to even configure the network. The iOS devices immediately "see" the reset brick, of course. With its right name. And all that. Just like they had zero trouble seeing the configured brick.
I'm completely out of ideas what could be causing this. Any suggestions from you guys? I'm game for running any diagnostics you might suggest - I'm actually a computer scientist, so I'm not averse to tinkering. Quite the contrary. But I cannot imagine any plausible technical scenario that causes the OS X machines (and only them) to lose the connection, so I have no idea what to try next.
BTW: there are unfortunately no Linux or Windows machines in the household, so I could not run experiments with other operating systems.

Answer 1

The Express / Extreme contains logs that can be examined for anything unusual. Unfortunately Apple does not provide details on deciphering them, but I could at least compare yours to what I think is normal. Several logging levels are supported.
If it is as old as you say, you might be able to experiment with earlier firmware versions. For example, I had an older Extreme that was very stable running Firmware 5.5.3 (I think) and upgrading it to a later version caused similar problems. A subsequent firmware version was required for a specific and unusual network client to function, but it resulted in the need to reboot the Extreme anywhere from once a week to twice a day. The only solution was to upgrade to a later model Extreme. That may be related to the phenomenon you are experiencing.
Experimenting with alternate firmware versions will be tedious though. Only a computer scientist would be interested
I doubt a new Extreme will give you the same problems. They have been rock solid serving a variety of clients: Macs, iOS, Windows, all sorts of others, zero problems.