I've seen this before myself and I've also seen the error that tells us that the destination volume is too small. This particular error message is misleading and has the tendency to create a 'wild goose chase' to resolve it.
I encountered the same message "error reading/writing to network". I traced the problem in the /etc/log/snapmirror log. The problematic SnapMirror relationship was identified by the "Request" then subsequent line "Abort (connection to destination dropped)". Once I had resolved that problem the errors stopped. In my case the destination volume was too small, an easy solution!