In the scenario you described, where two rockets initially at rest synchronize their clocks and then undergo symmetrical acceleration and deceleration, their clocks will not remain synchronized when they meet again.
This situation can be understood using the principles of special relativity. According to special relativity, the passage of time is influenced by relative motion and gravitational fields. When the rockets accelerate and decelerate, they experience changes in their velocities and, consequently, experience different gravitational potentials.
During the acceleration phase, each rocket's clock will run slower compared to an external observer who remains at rest. This is due to time dilation, an effect predicted by special relativity. As a result, the clocks on both rockets will show a smaller elapsed time than the external observer would measure.
When the rockets decelerate and come to a stop, they will have experienced different durations of acceleration and deceleration, leading to asymmetry in their proper times (the time measured by a clock in its own reference frame). As a result, their clocks will no longer be synchronized when they meet again.
This effect is known as the twin paradox. One twin who undergoes acceleration and deceleration will have experienced less proper time than the other twin who remains in a uniform inertial reference frame. Consequently, their clocks will show different elapsed times when they reunite.
It's important to note that the twin paradox can be resolved by considering the difference in inertial and non-inertial frames of reference, and by taking into account the effects of acceleration and deceleration on proper time.