Is there a maximum number of base stations in an extended wireless network?

My network configuration uses a number of older AirPort Extremes and AirPort Expresses solely as wireless-to-Ethernet bridges to extend my network to devices that only have Ethernet connectivity. Today, I tried to add another AirPort Extreme in bridge mode (you can see it greyed out in the attached screenshot) and my main router (the 11AC AirPort Extreme) simply refuses to see it.

If I disconnect one or two other AEBS bridges then the new bridge will connect, but the newly disconnected AEBS bridges won't reconnect. It seems like there's a maximum number of AEBSs that can be used in this configuration but I haven't seen it documented anywhere and if so, it seems like an arbitrary limitation. I was able to get six bridge devices to connect at once but I used a 4th gen AEBS in place of the 5th gen one I'm currently having trouble with. As I said, the problem isn't peculiar to a single AEBS because if I disconnect some of the other AEBSs I can get the newly added one to connect...but then the old ones won't reconnect.

Anyway, I've been trying everything I can think of (restoring the main AEBS, restoring the bridge AEBS, changing the AirPort Expresses to client mode, etc) and I just can't figure out how to get all six bridge base stations to connect to the main base station. This really seems to me like a firmware bug with the 11AC AEBS...is there something I'm missing?