Offline files - going offline unnecessarily

Have a Windows 2000 Server Appliance Kit box as a fileserver. Mapping to
share(s) on this server using DFS in an Active Directory environment.
(\\domain.tld\path\to\something) Everything seems to work just fine, with
the exception of offline files.

I have redirected My Documents onto the file server, on both my desktop
machine and a tablet PC. (So they have the same copy of My Documents.) The
desktop machine and the file server are always on the same subnet, connected
via different ethernet switches. Both run 100Mbps/Full-duplex. Periodically
my desktop machine goes offline for no discernable reason. I can make it go
offline by opening a Windows search window and searching for anything on all
local hard drives. (There's a short delay, the offline files balloon pops
up, then the search starts.) I can always reconnect by double-clicking the
offline icon and hitting OK.

I have three network drives mapped, all using DFS, all conincidentally
hosted by the same file server. The only item I have set to use offline is a
MyDocuments folder on one of the drives.

All I can think of that might cause this is a network condition, but that
seems a dubious possibility. I also tried bumping up the slow link value to
various values up to '10240' (1Mb).

Any other suggestions?

PS: What's the best way to suggest to Microsoft that individual shares go
offline and not an entire server? Or that Offline Files become DFS-aware?
i.e. when one of my DFS shares goes offline, they all do, because they are
all on \\domain.tld.