During Win Explorer copy: network name is no longer available

I have two machines connect to a Linksys Wireless Hub, XP
Home Edition (cable) and XP Pro (wireless). I share the
C drives on both machines. I can do Windows Explorer
copies (cut and paste) from one machine to the other as
long as it takes less than a few minutes. After a few
minutes, I always get "network name is no longer
available". If I immediately go to My Network Places,
Entire Network, Ms Windows network, My Workgroup, indeed
the other system is not visible. However, in a while, it
becomes available again.

Thanks