Hmmmm.. You have hit this NOT-A-BUG it seems. 🙂
If you change a global system variable, the value is remembered and used for new
connections until the server restarts. (To make a global system variable setting
permanent, you should set it in an option file.) The change is visible to any client that
accesses that global variable. However, the change affects the corresponding session
variable only for clients that connect after the change. The global variable change does
not affect the session variable for any client that is currently connected (not even that
of the client that issues the SET GLOBAL statement).
Refer this too. Read Shane Bester explanation.
You should change from the my.ini/my.cnf file and restart the server for the max_allowed_packet setting to take effect.