Tips for improving tuning stability on JPXI?

I love my 2011 JPXI. Great playability, killer tone. However, I need to tune after almost every song – and I have a fairly light touch and use the trem very little.

Any tips for improving tuning stability? I use 0.09 strings, so they shouldn’t be stuck in the nut or something like that.

Or is this just what I should expect from a floating trem? I didn’t have tuning issues on my Parker Fly Deluxe.