in fl studio 9.0.3 everytime i hit stop and then play, the unison lfo offset resets to it's default postion..
Is this on every project? It is possible that you accidentally did 'init song with this position' which will produce the behaviour you describe.
If this is indeed the case, then you should be able to fix it using the browser on the left - Current project -> Automation -> Initialized controls and you may be able to find and delete it from this list...
95% sure i noticed it in multiple projects.. at any rate i would've had to add the lfo offset to the list of automated parameters in order for it to be initialized with the song.. which i'm sure i didn't do.
that would've been the simplest explanation though.
will do further probing into the situation when i get home.