My iPod Touch was not connecting to my Airport Express router (which was "extending" a network as a WDS repeater) -- SOLVED!

Question

My problem was this. I have a large apartment with concrete walls, so just one wireless router would not work. I used apple Airport routers and used one of them (an airport extreme) to create my wireless network, and a number of other ones -- airport expresses -- to "extend" the network.
That's all great, but I found that a couple of my devices -- mainly my iPod Touch -- would refuse to connect to the repeater airport express routers -- it only wanted to connect to the main Airport Extreme router, not the satellite guys.
Finally I solved the problem.  It had to do with how the wireless network's configuration for "Radio" setting was set regarding 802/11 b/g, and the dual-band ability of the Extreme. Below is the description of how I fixed it.
======SOLUTION THAT I POSTED======
I've pretty much solved this problem. I do not FULLY understand why, but now I can have my iPod touch (and I am hoping my kindle) attach correctly to the satellite/repeater airport express.  Here is what I did:
I did two configuration changes to my central hub airport extreme router (i.e., the one that my other routers were merely configured to "extend.")  I realize now that these are both configurations that must be done at that central router, and the repeater routers then simply mimic or reflect accordingly.
-- First, I used the most recent Airport Utility (v6.0) and clicked on my main router (which, crucially, is an airport extreme that has dual band 802.11, both 2.4ghz and 5ghz.)
-- In the airport utility, I clicked on that Extreme router and then in its funky popup window, clicked Edit.
-- Clicked the tab called Wireless.
-- Clicked on Wireless Options button.
-- the first config change I made on that page was to change the Radio Mode setting to "802.11a/n - 802.11 b/g." 
     What nobody really tells you is that that hyphenated choice means that the 5GHz band will use the first of those two (namely, a and n, in other words the strong modern N standard will be used on this band ONLY) ... while the 2.4GHZ band will use only the second of those two, b/g, in other words, the devices that only can use that older weaker standard.
     So, it's kind of a segregation. I'm telling it "No, don't let the 2.4 ghz band try to handle traffic using N. That band will just take care of the old crappy clients."
-- the second config change that I made on that page was to check the check box to make a totally separate wireless network name for the 5GHZ band.  Further segregating things.  When I tried my solution without this additional step, my problem did not fix itself, though I don't fully see why.
As I said, a few questions remain in my head, but the darn thing works, so I'm happy. Among many other questions... are those airport expresses dual-band too? I didn't think they were but somehow they are repeating this dual-band strategy?  Whatever. it works.
BY THE WAY -- I recommend using the Apple question/answer board on StackExchange to get Apple-related answers. It is at http://apple.stackexchange.com/

Answer 1

To demonstrate, here's a screenshot from the Airport Utility on the iPod Touch in close proximity to the Express, still connected to the Extreme :