How can stop the concrete walking way sinking

Being on a hill, the soil will always tend to move down hill due to gravity. The house is built on un-disturbed soil and should not move. For the retaining wall to tend and move down hill tells me it was not built on undisturbed soil, or that it has water retention problems. There should be gravel and drainage on the up-side of the retaining wall. It could be collapsed, or plugged with roots, or non-existent.

Short of digging up and repairing the drainage field, sometimes just drilling 2" holes through the bottom of the wall every 4 to 8 feet will allow water to drain.

Look locally for someone offering services called "mud jacking" or "slab jacking." In general, they drill holes through the slab, and force concrete or similar material through under pressure, first filling any voids, then actually raising the slab. When it hardens, the new material continues to support the slab. Often, one or two rounds of such correction make a permanent repair. They can usually bring things back to the original position and with appropriate slope for water drainage or runoff. They may also be able to block entry of water for you.

It sounds like you have separation between your retaining wall and a slab walkway, and that the walkway is settling. Note that it does not matter if the native material or fill is behind the retaining wall, by removing the down hill soil support the uphill side was loaded against, you have installed a wall to resist that load with some degree of acceptable deflection (the wall will tilt until the soil it bears on provides enough support resistance to offset the wall loads). When a wall tilts away (or slides) you create a void that is filled with the soil that is pressing against the wall. Since you have a local increase in distance and a fixed volume of soil, the height of soil is compensated locally to maintain the approximate volume (the soil density will decrease locally also). As the height of the soil behind the wall compensates you have an apparent settlement in the soil (differs from standard settlements which are a natural densification of the soil). If the wall is relatively new, only few years old, the movement should subside as the foundation begins to resist the wall rotation and the tension in the wall begins to reach the acceptable deflection (if the wall is sliding you have a problem with the foundation of the wall that needs remediation). In such a case you can just back fill the void under the walkway slab and repair the slab (repairs depend on the degree of damage, mud jacking might be expensive solution for a walkway typically just replace the walkway). If however the wall was not adequately designed for the conditions, or conditions have changed beyond the design requirements, it could continue to move since the foundation may not ever resist the movement or soil is eroding away through an excessively porous filter. It is usually a wait and see thing when such problems are observed in a new wall, until it exceeds the acceptable design parameters for deflection. So what you should do I would suggest is obtain the plans and sdesign information, and see if you can determine what the design camber and deflection tolerance was anticipated to be. Then measure the existing camber of the wall.