I'm getting this problem too and trying to figure out what is causing it and how to prevent it. Any ideas are appreciated. Below are my notes.
20091003 - A hard drive named Earth on our Airport Extreme Network USB port has been occasionally giving the message "you cannot copy some of these items to the destination because their names are too long for the destination." which makes it so I can't copy files to it. This happens even with files with the name X. It is not a foreign language character name problem. The Earth is formatted MacOS with Journaling turned on. It happens to be a RAID 1 [Mirroring] drive but I don't think that is the problem. The problem does not happen when the drive is directly connected to a computer via Firewire or USB, only when on the Airport Extreme. I am using Tiger MacOS10.4.11 with everything up to date.
Running various disk utilities on it makes it look like it fixes the problem but really it is fixed because of turning the drive on/off/on or the remounting it on the network. There are no problems with the disk.
Turning the drive off is a temporary fix but the problem returns after a few hours and I don't like turning it off.
Restarting the Airport Extreme by doing and Update via Airport Utility also temporarily fixes the problem. I just used Airport Utility

isks:Filesharing and set "Airport Disks Guest Access" to "Read and Write". This may also solve the problem of the one MacBook Leopard MacOS10.5 of not being able to write to the disk.
Update: the problem is back so ReadWrite didn't fix it. I've been trying other setting adjustments to no avail. The problem seems to reappear after a while. I haven't found anything that is causing it such as access by one particular machine, etc. Letting the drive spin down does not consistently cause the problem either.
(Edit: I had written Express where I meant Extreme.)