There are several reasons why the liquid (water) may not oscillate and reach a stable height according to the Young-Laplace equation:
Inaccurate modeling of surface tension
Insufficient mesh resolution: In order to capture the small-scale features of the flow in the capillary tube, the mesh resolution should be fine enough. If the mesh resolution is not sufficient, the results of the simulation may be inaccurate, and the liquid may not oscillate and reach a stable height.
Inaccurate modeling of the contact angle: The contact angle between the liquid and the tube's walls should be accurately modeled in the simulation.
Non-linear effects: The Young-Laplace equation is based on the assumption of small deformations, but in some cases the system may exhibit large deformations which can lead to the violation of the assumptions of the Young-Laplace equation. In the case of larger deformations or capillary numbers, other models such as the Navier-Stokes equation or the Cahn-Hilliard equation should be used.
it may be necessary to perform experimental validation to ensure the simulation results are in agreement with reality.