So, we have an SE5 that won't initiate an Auto downshift, but paddle shifting works normally in both directions. However, even when manually downshifted to 1st, the engine won't idle and keeps trying to die at a stop. I'm actually more interested in that because a lot of throttle manipulation, depending on how you're doing it, can interrupt the Auto downshift initiation.
So, what is the engine idle behavior in Neutral? Is it hard starting, idle rough, idle fast, keep trying to die? Does it run normally at higher RPM? If so, typical symptoms of a large vacuum leak such as failed purge valve or hoses to the MAP sensor. Vacuum hoses is always the old standby here, anyway. Your machine is 4 years old. Any codes? Check Engine Light? Just need to divide and conquer a little and separate the issues.
If idle operation is normal, what happens when you shift to 1st. Hard shift, feel like the centrifugal clutch is dragging on the engine at idle? Or after you start moving does it feel like it's not disengaging? Well, that would be a worse problem and probably a trip to the dealer is required. Or, are things relatively normal after startup, and the problems start after riding for awhile?