Windows ME and Yahoo Messenger Timing Out

My mother's computer has Windows ME, and she uses Yahoo Messenger to chat with
me, and with my siblings periodically. Let's not get into the subject of
Windows ME, I know it sucks, but a Windows XP upgrade, right now, is not a
possibility.

I have my Yahoo Messenger (V6.0.0.1750) online 7 x 24. When she brings her
computer online, and starts her YM (also V6.0.0.1750), I know it. When YM is
loaded on her computer, but she's not actively using it, it seems to time out -
my computer tells me with alert sounds when her YM goes offline and comes back
online.

Generally, if she leaves YM running for more than 10 minutes, her YM will go
offline, and come back online, sometimes off-on-off-on in a 15 second stretch of
time. Repeatedly. Even when she's using the computer, but not YM.

Right now, she's visiting with me, and I have her computer sitting across the
room from my computers. My 3 computers, and hers, are all connected thru my
Linksys BEFSX41 (at home she connects thru a SMC 7004ABR). In the 15 minutes
since I started typing this, her YM has gone off then on twice. And she's in
the other room.

I've asked her about this situation before, but she doesn't notice a thing while
she's at her computer - it shows no symptoms when her YM goes offline. This is
the first time we've had the chance to examine the problem while in the same
room.

I've checked her YM configuration, her network configuration, and her power
options. No setting anywhere that says explicitly to drop network connection
for any reason, that I can find.

Any ideas?