One of the shell context-menu extensions installed on your system is probably accessing the network whenever it's being called.
In the past I think this has been seen with one of the source-control extensions (Subversion or ClearCase or CVS) but I can't remember which one.
If you're not sure which it might be you might want to try using FileMon and RegMon to see what's going on when the network access is happening.
You can also remove some or all 3rd party items from the context menu, or move them into a sub-menu, so that the menu is both faster and more organised: