I have the same problem with an N707 (lack of sound from headphones). However, applying a little downward pressure on the headphone jack makes the connection and everything is fine. Leads me to think the fault as being a dry joint or cracked circuit board track - as has been suggested before in this thread. Taken the case off but everything inside is far too compact and small for my soldering abilities.
My solution - small plastic plate with precisely cut slot for the unit and room for a tiny wedge to apply just enough pressure on the multi-functional unit connector to make the connection, and then plug the headphones into the control unit.
Alternative to consider - short length of plastic ‘channel’ into which the unit slots (other side to connector) and an elastic band through a hole in the bottom of the channel, then looped over the headphone jack, pulling it down slightly.
Not pretty but it works.
Is this a common fault?