Mapped Network Drive dsconnects when uploading to the Internet

We have 4 computers that all run new versions of Windows 7. Each have been connected to a Mapped Network Drive and they all connect fine to the network. Dragging files throughout windows works fine. When we try to attach a file from the network in the browser (as in a GMail message) or upload a file with FTP it disconnects us from the network and from the Internet.

This only happens with 2 of the 4 computer.

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