Dang. I accidentally posted an incomplete reply, tried editing it, and apparently took too ****** long.
Here is the complete post:
Okay, I have been experiencing the OP's issue for a while now—but only on one of two MacBook Pros. Both have SL 10.6.8. Both use WiFi. Both have the drive mounted in the background with no user-initiated read/write processes (who knows what sort of indexing or other task is going on in the background). Oh—it should be noted that this is a USB, non-TC drive, and I do not currently use Time Machine. There is no hub, etc.
On the 2006 MBP 15", the USB drive never loses its connection. I never get the "server connection interrupted" message. On that MBP, I have an alias to the drive in the login items (under Accounts). There is no problem with the AEBS shared drive when accessed from this computer.
On my MBP 17" (late 2010), I do not mount the drive at login. When I want to access the drive, I go to the sidebar, click the triangle next to "Shared," select my AEBS, and the drive shows up as a folder icon. I click once on the folder (in column view the whole time), and the drive icon shows up as mounted on my desktop. I can read/write to it without a problem (though I do so for occasional, manual backups). It is in this scenario with the MBP17 that I begin getting the continual "server connection interrupted" messages. Again, I don't use Time Machine, and this is a LaCie 1TB drive connected via the AEBS USB port. The error pops up for me when the drive is just mounted, idly in the background doing nothing.
Because it works fine on the MBP15, I can't fathom that it's a hardware issue with the drive or the AEBS. After checking Console for messages, adding it as a login item in my account on the MBP17, running software update (just Safari and iPhoto updates), and doing lots of searching, I couldn't fix it, so I quit trying. But during my investigation, I noticed that if I access the drive in a different way, it changes the icon of the drive when it is mounted on my desktop. When I access it via the sidebar, as outlined above, it has drive icon but with a WiFi symbol. When I get to it the other way, it has a drive icon with people symbol (meaning "shared," presumably).
Anyway, the AEBS drive has been mounted for 6 hours today in the background on my MBP17, and I have had zero "server connection interrupted" messages! None.
Here is how I accessed the drive. In sidebar preferences, I selected "Show MacBook Pro" (it's the top level, akin to "My Computer" on Windows). I click on MacBook Pro in the sidebar, then "Network," then AEBS, then the drive. Once the drive mounted (with the people icon), I dragged it into my login items. It works. I don't know why, and I don't know why the icons look different, because when I view the drive info, the server address is AFP—no matter how I connect to it. I also tried "Connect to Server," but that yielded the same result and the same drive icon as going through "Shared" in the sidebar.
I confess that though I'm very tech savvy, I know just enough to be dangerous when it comes to networking. I remember having to use the Chooser to get to stuff like this, so this is all quasi-mysterious to me. I mean, I know the basics, but that's about it. The only thing I thought was significant was the fact that when I accessed the drive via Sidebar>Shared>AEBS and it displayed as a folder (with the same people icon on it), when I'd would get info on that folder, it said the format was "Sharepoint." I thought Sharepoint was some Micro$oft technology? Anyway, when I get info on the drive mounted using the method that doesn't cause those messages, it says the format is AppleShare.
Weird, huh? Well, I hope it gives someone experiencing these messages some insight or clues. Oh, and I am running 10.6.8 on both Macs (we have an all-Apple household; no Windoze), and my AEBS firmware is 7.6.1.