thanks for the interesting idea! I didn't even know the Nintendo DS 
has a browser ;-)

The session terminated message only appears if the JavaScript was 
unable to get a positive status response for the current session ID 
twice in a row. Here's what happens:

1) You log in. 
2) Remote Buddy saves the session ID in the log in form as authorized. 
3) The session id ("sid") is now transfered with *each* request to 
Remote Buddy, authorizing it to access dynamic content. 
4) a background timer makes a http query every few seconds for 
"sidValid.rmbd?sid=.....". 
5) Remote Buddy will either reply with yes (inidicating the session 
is authorized) or no (the session is no longer authorized, i.e. 
because you restarted Remote Buddy) or not at all (i.e. Remote Buddy 
quit or computer or network were shut down). In either of these 
cases, the "Session terminated" will appear, so users don't get 
confused with nonfunctioning interfaces.

What could help debug this is the debug output you can make Remote 
Buddy to generate in Preferences > Hardware > AJAX Remote > Output 
accesses and debug info.

You can then see the ouput via /Applications/Console.app.

If you send me that output (do *please* search for your password in 
that output, though - or set a dummy password prior to setting that 
option as it'll otherwise and unavoidably be part of the output), I 
can have a look at what queries the DS browser is making - or not 
making, and then base further work on that.

And then, there's another possibility: the "session terminated" image 
is loaded on each and every loaded page (except login of course), but 
set to be hidden by default through a CSS attribute (display: none). 
If the Nintendo DS ignores that CSS attribute, you'll see it 
irrespective of whether the session is actually considered valid or 
invalid by actual code.

Best regards, 
Felix