Ta dA!! and poof goes a cloud of smoke and a weak and frail little man apears!
Ok, so i see you live in mexico city. is that the one in mexico, or is there a mexico city somewhere in the US (hey texas has a paris)?
Here is what is causing your issues. As mentioned by global_recon, as your stator gets hot, it produces less juice. This combined with the fact the bike is at a drain at idle that is what cause ur dying. Here are some things that you can do to help, not fic, just help.
1) either replace your tail with led arrays (radiaz (sp) makes some decent ones), or when at a full stop take your hand off the brake... this saves about 30 watts (2.5 amps) of juice.
2) another thing, turn off all accesories. If you encounter traffic often you may even want to purchase and wire a switch for the headlight. that is 55 watts saved.
if you do both 1&2 that should cover you for when the fan is running somewhat. The other issue is the stator. when you have it replaced, have them do an extra turn or 2 per pole, and that will fix the idle draw.
1)watch your bat water levels, heat from the GB can cause it to run dry frying the system.
2) a r/r relocation, or GB removal will prevent further damage from long idles.
3)HEAT DESTROYS STATORS!!!!!!!! FIND AN ALTERNATE ROUTE
I think this will save you much time down the way. not only that, but you will prolly get home sooner too! There are a few gps with realtime traffic if you are interested.