You realize that you are not talking directly to Apple employees ... correct? We, like you, are just Apple product users.
In your case, I would suggest that you first download and install the earlier firmware version. Let your network stabilize, and then, retry upgrading to the latest version to see if the first install did not take properly.
I have Airport Express and had similar problems, so I downloaded and reinstalled 7.6.1 (never got 7.6.2).
The following includes instructions on how to install older versions of Airport firmware:
Hope that helps.
I am having the exact same issue.
We have an extended network in office (2 latest apple airport extremes).
And a similar extended network at home (1 older airport extreme + 1 time capsule + 1 older airport express).
Both are configured similarly with WPA2 security and default dual-band (bridge across 2.4 GHz and 5 GHz)
On both the networks, we are seeing increased issues of disconnection since upgrading to 7.6.3.
The network does not go down but the extension does not work. We are seeing the same error for both networks:
"This base station was unable to extend the network..."