This is the same issue as 16.04 LTS wifi connection issues
but I am not allowed to add a comment to that post.
PC: Dell Inspiron 6400 laptop, Intel T7200, 2GB RAM, Intel PRO/Wireless 3945ABG [Golan] (rev 02)
With Ubuntu 16.04.2 LTS, as of 18th march 2017, I still have this problem. The WiFi indicator (top right of desktop, between DayOfWeek/Time and Sound icons) disappears and the WiFi connection is lost.
The workaround suggested by eldosoa works about half the time for me.
sudo service network-manager restart
On those occasion that the above workaround does not work for me, closing the lid of the laptop, allowing the laptop to go to sleep and opening the lid again to re-awaken restores the WiFi connection and the WiFi icon is also restored.
Note that the network manager restart command, as suggested by eldosora, must have already been tried for this to work.
So far, this has worked for every occasion that eldosora's suggestion does not restore the WiFi connection.