What can you do when your homeowners insurance company does not pay on a burglary claim?

It depends on why they didn't pay the claim.

If you have the coverage and followed the requirements, like making a police report, cooperating with the insurance company as well as the police then you should have no problem with a claim, if it was in fact a theft.

Otherwise you can always sue the company or file a complaint with your state department of insurance if you feel you were denied coverage you paid for.