Convergence of results (static stress analysis)

Are the displacements converged?

If not, deal with that first.

From there, ask yourself if convergence is really possible. At sharp corners there will be singularities that will not converge.

Start there and then post some screenshots of your model and where you are seeing problems.

For some reason the assembly expects parts different from those that you included in the zip file so I can't open your files.

But as Jared pointed out, if displacement converges while the stress continues to increase with finer mesh, it's likely that you have a stress singularity. They often occurs close to fixtures (infinite stiffness) or at sharp inner corners where you'd expect a radius on the real part. With singularities, stress will continue to rise towards infinity when you refine the mesh.

What you can do?

Either change the geometry or the fixture to better reflect the "real world part" or see if the stress converges in the vicinity of the singularity and if so, use this stress value to draw your conclusion.

Good luck.