I just purchased a brand new JTV59 from Sweetwater and it has the same issue right out of the box. When I first tried it it was cold from being in the delivery truck. After is warmed up, the problem went away. The next morning it was back. After being plugged in for a couple of hours to the power supply it was fine again. I was suspecting a cold solder joint on the switch and removed the cover. The black wire at the top has a dull solder connection, which could be the culprit. Rather than taking a soldering iron to a brand new guitar, I contacted Sweetwater and they arranged to replace the guitar. If your guitar is out of warranty, I would look at the connections, or enter a ticket with Line 6. It's always better to have a trained Technician work on your guitar.
PS: I also have a v700 that I love.