Okay - Here are my results of extensive testing today - repeatedly copying my iTunes and iPhoto Libraries to the TimeCapsule (SMB and AFP) , to a D-Link DNS-323 NAS (SMB only) and to a Western Digital MyBook Live 3-TB NAS (AFP and SMB).
I had these copies going in all directions - two different Macs (iMac and MacBook Pro) - wired - all day long - but only to shares mounted via SMB - to my various NAS drives including the Time Capsule. There was not one occurence of the Disconnect popup during 6 hours or so of copying (iTunes library about 30 gig - and iPhoto about 12 gig). I disabled Time Machine backup during this testing to avoid having it confuse the test results.
In the middle of the afternoon the - I switched over to AFP mounted shares - I did an AFP mount on the MacBook Pro to the WD MyBook Live drive - copied the iPhoto library over to it. No popup. Then on the iMac - I did an AFP mount to the Time Capsule and copied the iPhoto library to the Time Capsule. Copy was successful - but within two or three minutes of the copy completing - the Disconnect warning dialogue popped up on the iMac (not the MacBook Pro) and continued popping up at the following times: 14:58, 15:31, 15:50, 16:00, 16:17, 17:48, 18:17 and 18:57. No messages in the TC log. No active transfers to or from the TC during the subsequent popups. Currently I have logging level set to 6 (Info) - now setting it to 7 (Debug) and will try again tomorrow.
Obviously my test results are pointing to the issue being with the Time Capsule and/or the firmware upgrade (since SMB all day long did not have an issue on the TC or the DNS-323 - with constant data transfer occuring over a wired connection - as well as AFP and SMB working fine to the WD MyBook Live).
I believe that Apple made some type of change in the AFP specification starting around 10.6.8 (Snow Leopard). Not exactly sure what they changes were - but could be a factor here - meaning that Macs on the latest (and last) version of Snow Leopard may be seeing the impact of the AFP changes.
My MacBook Pro and MacBook Air are typically connected wirelessly and usually through the TC vs my other access points. This week I have the MacBook Pro wired (with Wifi disabled). I did initially notice some wireless issues with Lion - but those seem to have disappeared with OS X 10.7.2 - or at least I am not noticing.
I believe I now know how to reproduce the Disconnect popup - and hopefully logging level 7 may show something when the Popup occurs again.
~Scott