Hi motodude62,
The GPS ( "NAV" ) dedicated Power Supply is provided from the Audio Unit circuit.
This sounds very much like a KNOWN problem with the first release of Audio Software
for the US & Canadian Market Audio system ( only ) that has the XM Satellite Radio.
The problem was that the Software would intermittently fail to shutdown when the Ignition
was switched off and continued to draw power - draining the battery.
The solution is simple - Check the Audio Software Version you have, as below.
Turn the Ignition ON ( but don't start the engine ) and switch the Radio OFF
( Volume all the way down to Minimum, Mute and Off ).
Turn the Ignition OFF, wait for everything to shut down, then turn it ON again
without starting the engine.
Press and hold the "P" button until the "DIAGNOSTICS" menu is displayed.
Scroll to the S/W VERSION item, and press Select ( "
i" ).
The "old" Version was 1.04A - If this is what your Version is, then it explains your problem,
and it needs updating to Version 1.04E.
ALL Triumph USA / Canadian Dealers "should" know about this -
IF they read all the Circulars from Triumph !
A Number of Forum Members have had problems with Triumph US Dealers being unable to find
the Software Update on their system, and this Topic was posted to explain to them how to find it ! :
Where Triumph dealers can find audio software updates ( U.S. )The next hurdle you might encounter is a Dealer trying to charge a fee for the Software update,
but if you can demonstrate that the Trophy has been serviced by a Triumph Dealer at any time
since the Software Update was released ( as long ago at least as November 2014 ) then you would
have good grounds for insisting you are not charged for the update as it should have been carried
out as part of any normal Dealer Service, without additional cost, as it was a "fix" for a known issue.
If you encounter any difficulties with this, send me a Private Message and I will give further advice.
Meanwhile, until you get this sorted, when leaving the Trophy parked I recommend removing
Fuse No.3 ( 10A ) from the Front Fusebox behind the left side cover, which is for the Audio System,
and this will stop any further battery drainage from the Audio System when the Ignition is off.
Cheers

