Thanks for all of your help Toz.
I think this may be a bug in xfce or nm-applet.
After doing a complete reinstall, the icon was back. After re-applying my xfce setttings which I backed up from ~/.config/xfce4, the icon disappeared again.
After some fiddling around, I found that if I had the notification area in an horizontal panel the icon was visible, but if I had it in a vertical panel it would disappear.
I ran your commands regardless, in case you can glean from them which package I should be reporting the bug in.
Code:
mark@eeepc:~$ cat ~/.xsession-errors | grep -i nm-applet
** (nm-applet:2678): DEBUG: old state indicates that this was not a disconnect 0
** (nm-applet:2678): DEBUG: foo_client_state_changed_cb
** (nm-applet:2678): DEBUG: foo_client_state_changed_cb
mark@eeepc:~$ cat ~/.xsession-errors.old | grep -i nm-applet
** (nm-applet:2183): DEBUG: old state indicates that this was not a disconnect 0
** (nm-applet:2183): DEBUG: foo_client_state_changed_cb
** (nm-applet:2183): DEBUG: foo_client_state_changed_cb
nm-applet: Fatal IO error 11 (Resource temporarily unavailable) on X server :0.0.
mark@eeepc:~$ sudo service network-manager status
[sudo] password for mark:
network-manager start/running, process 708
mark@eeepc:~$
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