AppleCare actually overnighted a replacement Time Capsule last Thursday - and I received it in less than 24 hours - quite impressive !!!
However, the replacement Time Capsule was identical to my existing Time Capsule - a 2TB 3rd Generation. It shipped with 7.5.2 firmware. I kept it on 7.5.2 for about a day. The disconnect popups still occurred but with very low frequency and most of the time they occurred only once after any Mac with an AFP-mounted share would wake from sleep - and no repeat again. I also had the existing time capsule set up as well - but on 7.6 firmware - identical behavior.
Somehow with all the resetting and reinitializing of the two TC's - the frequency of the problem has diminished - with the only difference being the fact that both Time Capsules were completely erased and reformatted as well as reconfigured. It is becoming harder for me to reproduce the popup - on both Time Capsules.
I use my Time Capsule in bridge mode - and have always used it that way. Out of curiousity - I have tried every configuration under the sun - including using the TC as a router - plugged directly into my cable modem in the basement and even setting it up as a stand-alone wireless TC - and even going to the extent of setting it up to distrubute a range of IP addresses - with my main router redirecting the DHCP server request to the DHCP server on the TC. For this to work - I had to use a LAN port (and not the WAN port) on the TC. The DHCP part worked just fine. Still - the same results - which is now only an occasional popup after wake from sleep.
On the following day I upgraded the replacement TC to 7.6 - still identical behavior.
I then decided to install an earlier version of Snow Leopard (10.6.3 and 10.6.4) onto an external drive and boot up my MacBook Pro and MacBook Air (with 10.6.3 and 10.6.4 - respectively) - and without applying any updates - to be sure to keep OS X earlier than 10.6.8 (where I know the problem will occur). Had I realized that you can install Snow Leopard directly to a USB or Firewire drive - I would have done this much earlier.
I mounted an AFP share on the TC from 10.6.3 and .4 - copied my data - waited - watched - put the machine to sleep - even turned off the wireless in one scenario and pulled the network cable in another. Surprise Surprise - no popup in any scenario !!! It appears that prior to 10.6.8 - that there are no popups - and after waking from sleep (after having copied sufficient data to the AFP share) - instead of a popup - the share would simply (and quitely) unmount itself - not providing any indication that something was wrong. This problem had apparently been happening to me all along - without me knowing. Looks like Apple added the popup feature in 10.6.8 to notify of the break in the network connection - so now it telling us when the issue occurs.
I can understand the popup occurring when I actually go out of wireless range with a MacBook - or I "intentionally" pull the ethernet cable (for purposes of testing). But - waking from sleep - should restore the network connections without complaining or warning - unless the network connections take longer than usual.
I keep my iTunes and iPhoto libraries on my iMac - and had been copying them to the Time Capsule about once a month and then replacing the iTunes and iPhoto libraries on my MacBook Pro and Air - so that they would be fairly current when traveling. I did not randomly start copying the libraries to the TC out of the blue - I was doing this on a regular basis for about a year and never noticed any problem.
Also - with an SMB share mounted on the Time Capsule - you can actually shutdown wireless or pull out the ethernet cable (on both 10.6.8 and 10.7.2) and it will not complain - until you actually go into the share and attempt to access a file within a folder - at which point you will get the Server Connections Interrupted popup.
In reporting these latest findings to my AppleCare case rep - he also reported back to me that there are changes in 10.7.3 that address the network connectivity slowless after wake - that may just solve this issue - at least for me - as he is thinking this may be specific to 3rd generation Time Capsules.
10.7.3 should be out very very soon - and I will test again when it comes out. I realistically can't invest anymore time on this. The TC is working fine for Time Machine backups - and that it what I primarily use it for.
~Scott