Computer disappears midstream

I have a home network consisting of a laptop and a desktop. When I
boot up the laptop, the display of MS Home under "My Network Places |
Entire Network | Windows Network" shows both laptop and desktop
listed, and both function fine in either direction, to copy files,
list files, etc.- After a short time, doing other things, I find that
the Laptop has disappeared from the MS Home display, on both
computers. - The machines can both ping each other, and the laptop, if
it asks to list the desktop files shown under MS Home, can actually
copy a desktop file to the laptop. But not vice versa, since the
desktop can no longer see the laptop. - What's going on - and better,
is there any way to fix it? - Thanks.