The ignition switch recall may have nothing to do with this problem but it's a recall that should be addressed regardless. I don't know the 2003 version but I'd not be surprised to find that the dealer doesn't know what the real problem is. Sadly, it's rare to find a motorcycle dealer who knows much about scooters.
See
http://www.suzukicycles.com/~/media/Recalls/AN400%20650IgnitionSwitch.ashx9/7/2005 - 2003 and Certain 2004 AN400/650 Ignition Switch Terminal Case Replacement
RE: Recall Campaign for Ignition Switch of AN400 and AN650
Affected model and VIN range
AN400K3 32100005 Nov 11, 2002 to 32102014 June 2, 2003
AN400K4 42100001 Aug 5, 2003 to 42101092 Jan 9, 2004
From
http://www.motorcyclistonline.com/motorcycle_recalls/49/2003/suzuki/an400_burgman/36695.html:
Recall ID #36695 - ELECTRICAL SYSTEM:IGNITION:SWITCH
Recall Date
AUG 29, 2005
Motorcycle Affected
2003 SUZUKI AN400 BURGMAN
Summary
ON CERTAIN SCOOTERS, IF THE IGNITION SWITCH IS NOT FULLY TURNED FROM THE 'OFF' TO THE 'ON' POSITION, THERE MAY BE UNSTABLE CONTACT BETWEEN THE IGNITION SWITCH CONTACTS. THIS CAN CAUSE ARCING IN THE IGNITION SWITCH.
Consequence
HEAT FROM THE ARCING CAN MELT THE INTERNAL SWITCH BASE PLATE. IF THE SCOOTER IS RIDDEN IN THIS CONDITION, THE IGNITION SWITCH MAY FAIL. IF THIS HAPPENS, THE ENGINE WILL STALL, THE LIGHTS WILL GO OUT, AND THE OPERATOR MAY BE UNABLE TO RESTART THE SCOOTER. THIS COULD RESULT IN A CRASH.
Remedy
DEALERS WILL REPLACE THE IGNITION SWITCH TERMINAL CASE ASSEMBLY FREE OF CHARGE. THE RECALL BEGAN ON SEPTEMBER 7, 2005. OWNERS MAY CONTACT SUZUKI AT 1-800-255-2550.
Potential Motorcycles Affected
5869
Notes
AMERICAN SUZUKI MOTOR CORP. 2082
Also an on-line version of the service manual for this bike popped up (may be of use to this rider in the future):
http://www.slideshare.net/guestcc7e80/suzuki-burgman-400-2003Not much in there about the ignition switch but it physically looks pretty much like the more recent ones.