How to refresh the shared list in the Finder's side panel?

Relaunch the Finder

option+right click [or Ctrl+Opt+left click] the Finder icon in the Dock, last item is Relaunch.

Or try this I found on StackOverflow Automator Command to Refresh ALL Finder/all Finder Windows - works for Finder windows, can't test for Shared items.

tell application "Finder"
    set theWindows to every window
    repeat with i from 1 to number of items in theWindows
        set this_item to item i of theWindows
        set theView to current view of this_item
        if theView is list view then
            set current view of this_item to icon view
        else
            set current view of this_item to list view

        end if
        set current view of this_item to theView
    end repeat


end tell

Or use Terminal app to performing it manually

killall Finder

Also turning WiFi off and back on should refresh the shared list.

I've just had the very same problem (OS X El Capitan) and refreshing the Finder didn't work out for me. Neither turning off and then back on the WiFi.

What worked for me was restarting the router.

If the remote machine is not listed in Finder window, try this:-

Click on the Apple icon (top left) and look through "Recent Items" list, if the share is listed, simply click on the share name and it will automatically re-appear in Finder.

Obviously this will only work if you have not cleared the recent items list!

Hope this helps.