This is one of the main reasons I tend to avoid under-saddle piezo pickups. I've had a few ABG's with this issue as well as nylon string classicals... including a few brand new ones, still with factory strings. It's just too frustrating of a system for me, especially since I'm not crazy about the tone either. I prefer K&K style acoustic pickups.
I feel like it's also worth mentioning that I have had output and tone consistency issues with several sets of TI flats, even on electrics with magnetic pickups. Gave each set plenty of playtime to break in too, but to no avail.