Synchronized Clocks in Inertial frame Will the synchronized clocks placed in an inertial frame remain synchronized forever?
 A: Yes.  
Assuming, of course, they are mathematical clocks and this is a thought experiment in flat spacetime.  Reality introduces too many unquantifiable variables.
They will drift apart under the influence of any acceleration in the direction of their displacement from  one another.
If  they are held a fixed distance apart in their own reference frame, the time difference between them will add up the accumulated acceleration they experience or 'feel' in their own reference frame.
A: Yes, they will.
"Synchronization" in a strict sense means that both clocks are  said to define  one and the same inertial frame. At the moment of synchronization they are said to share same velocity and direction.  They will carry the inertia defined at the moment of sychonization with them, all the time. Any acceleration one of the synchronized clocks will experience will be the same acceleration as the other one experiences under the same circumstances within the defined frame.
To test this statement imagine one clock in a sports car, the other one as a stationary clock. The fact that a pendumlum measuring time will be accelerated in the sports-car thus differing from a pendumlum in the stationary clock does not spoil the synchronization as any change due to acceleration  can be dealt with calculating (Lorentz transformation).
If it's not mechanical pendumlum and movement that  is being used to measure time but the speed of light there are not even divergent accelerations of clocks in respect of velocity to be calculated upon as  light cannot be accelerated beyond the speed of light. However changes in respect of the once defined direction of the light beam have to be considered ("time delation").
This shows that inertial frames are being defined by synchronization (in a very narrow sense). A defined inertial frame will remain defined, as you can always calculate on any acceleration any participating particle experiences, be it a clock.
