System Information
Operating system: Windows-8.1-6.3.9600-SP0 64 Bits
Graphics card: GeForce GTX 660 Ti/PCIe/SSE2 NVIDIA Corporation 4.5.0 NVIDIA 461.40

Blender Version
Broken: version: 2.93.0 Alpha, branch: master, commit date: 2021-03-20 21:00, hash: rB9ca67c47a152
Broken: 2.90
Worked: 2.83.9 (bonestudio build)

This broke somewhere between rBaed11c673efe and rB1d4bae856690 (I assume rBb18c2a3c413b: EEVEE: Refactor of eevee_material.c)

Short description of error
Create few objects, add glass refractive materials (0 roughness to see clear) to all of them
enable SSR for Eevee and for materials. Try to change SSR depth for 1st created material. Then for next.

SSR depth works only for all materials and can be changed only at 1st refractive material.