The answer to your question depends on which part of "stable" you are interested in. The height of the orbit does not change much, atmospheric drag can be neglected almost completely. The orbital lifetime is in the order of many many thousand, possibly millions of years.
On the other hand, the precise orbit is not stable but varies over time. Gravitational influence of the Sun and Moon cause a change of inclination by almost one degree per year - see Why is the ribbon of decommissioned geosynchronous satellites skewed?. If you want to dive into the dynamics of these orbits, here is a nice PDF with details.
Another major influence on the orbit is the radiation pressure from the Sun. As the orientation of the decommissioned satellites is not fixed, the pressure can be estimated to be equal in all directions (averaged over time). Hence, it does not lead to orbital decay, but orbital perturbations only. For this reason, the height of the graveyard orbit is adapted to the surface-to-mass ratio of the satellite: The higher the expected influence of radiation pressure, the higher the desired orbit.
In summary, a typical graveyard orbit is about 300 km above GEO, consisting of
- 200 km space around GEO to be kept free
- 35 km additional to cope with gravitational disturbances
- plus another 50 - 100 km for perturbations due to radiation pressure, depending on satellite structure