My JTV-59 when I have it in a modeling mode sounds like it is kicking in and out of the chosen guitar. I will be playing around in a certain type of model and it sounds like it kick to another model or the analog pickups.
Look through this forum. The switch is a well-known problem on the JTV-59. They are replacing all the switches on the JTV-59 so you have to find out if yours has the old or the new switch. All JTV-59s going on now have the new switch, but if your JTV-59 arrived more than about 4 weeks ago it probably has the old switch. Call Line 6 Support.