There is nothing "wrong" here, but the problem is that 3rd Express is not repeating the signal from AE2. It can't since you can only "extend" the wireless signal from the main router one time.
In other words, Apple's "Extend a wireless network" feature works like the hub and spokes of a wheel. AE1 is the "hub" on your network and AE2 is a "remote" and the end of a "spoke". The remote connects directly to the hub through the spoke.
You can have other remotes at the ends of other spokes on the network, but each one of them connects directly to the hub....not to another remote at the end of another spoke.
AE3 in your case is located closer to the AE2 than it is to AE1. Since AE3 is picking up a signal from AE2 at the end of a "spoke", it cannot extend it again. It can "join" the signal for use with AirTunes or a remote printer...but it provides no additional wireless signal coverage when it joins.
If you want AE3 to "extend" you will need to see it displayed on the graphic as connecting directly to AE1. If you do this, you will see that both AE2 and AE3 are connecting to AE1.
Thank you very much Bob. I suspected this limitation but Apple does not make mention of this in their documentation. Most articles state that everytime you repeat a signal in my configuration, the throughput speed is cut in half. Not that in fact it is not possible after one repetition. A hub and spoke model or star configuaration is not feasable here because of the range it has to cover and a lot of concrete walls.
I suspected this limitation but Apple does not make mention of this in their documentation.
It is there, but Apple doesn't take much time to talk about it.
It might be a bit clunky, but you could come out of the Ethernet port on AE2 and wire to AE3 if feasible. Setup AE3 to create a wireless network using the same wireless network name, security, password in Bridge Mode and it will effectively "extend".
... I suspected this limitation but Apple does not make mention of this in their documentation.
If another extended Wi-Fi base station ➋ is placed between the primary Wi-Fi base station ➊ and the extended Wi-Fi base station ➌, the extended Wi-Fi base station ➌ will not allow clients to join it. All extended Wi-Fi base stations must be in direct range of the primary Wi-Fi base station
It is also untrue that "everytime you repeat a signal in my configuration, the throughput speed is cut in half. " This was true for WDS but not with an 802.11n "extended" network. The throughput is reduced but the effect is much less than 50%.
The fact that you have a lot of range to conver including concrete walls means that you will have challenges with "extending" a network wirelessly. Wireless signals will be attenuated by such structures. If you can find a way to create a "roaming network" your troubles will be over.
not sure if you have figured out the solution or if this even solves what you are trying to do, but here is what i suggest. i also saw another post of yours with a time capsule, so i will include it in my solution (or more of a suggestion, really) and you can switch things up as they work out. here is the concept of my idea..
HOPE IT HELPS!! i have no idea if this works, as i am far too poor to afford so many apple products HA