Are there any specific error messages or warnings displayed when the instability occurs? Also, please try adjusting some of the import options mentioned in the documentation (URDF Importer — Omniverse IsaacSim latest documentation).
This is an old post, but the issues on self-collision after URDF import have been fixed in Isaac Sim 4.5.0 as shown in the video below using the H1 inspire asset:
Update to Isaac Sim 4.5.0 or Later
This version includes specific fixes for self-collision issues after URDF import.
Disable Self-Collisions for Problematic Links
Modify your URDF to turn off self-collision for parts like fingers, which often cause instability due to overlapping collisions.
Review and Correct Collision Geometry in URDF
Ensure that all collision meshes are accurate, non-overlapping, and properly scaled, especially for moving parts. Use simpler collision shapes where possible.