Disclaimer: The materials provided below are informational and should not be relied upon as legal advice.
If your storage agreement provides that the storage company has a duty to provide security and/or security cameras, then you can sue them for breach of contract. If you believe the storage company had reason to believe your adjoining neighbors would break into your unit, but did not take any steps to prevent this, you may be able to sue them for negligence. Either way, you should submit these losses to your insurance carrier(s), if you have purchased any insurance policies. Be sure to consult your own attorney to protect your legal rights.
As my colleague stated the wording of your contract needs to be reviewed. I am an attorney in Fresno and offer free consultations if you would like me to review your contact and discuss the matter with you.
Note this answer does not constitute legal advice, and should not be relied on. Each situation is fact specific and court specific, and it is not possible to evaluate a legal problem without a comprehensive consultation and review of all the facts and court pleadings filed in the case. This answer does not create an attorney-client relationship