There is no way to answer your question without knowing the specifics of your situation. However, if you do not have an attorney representing you in this, you should definitely get one as that will make it easier to resolve your case.
Probably because you don't have an attorney; among other possibilities
Personal injury cases only; I'm good at it; you be the Judge! All information provided is for informational and educational purposes only. No attorney client relationship has been formed or should be inferred. Please speak with a local and qualified attorney. I truly wish you and those close to you all the best. Jeff
If you have a spinal injury you should definitely hire a lawyer. By not hiring a lawyer you may be playing into the insurance companies hands, hence the rejection of the certified mail. Most of us charge reasonable fees and are willing to speak with you without an upfront payment.
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You do not state where the incident occurred. If in California there is a 2 year statute of limitations on a personal injury claim against a private person or entity (i.e. non-governmental). If you suffered personal injuries, it my opinion it is a mistake to try and represent yourself unless the "spinal injuries" are very minor. It is possible you are sending the letters to a PO Box versus a street address. Certified mail cannot be left at a "drop" location, someone needs to sign for it.
I suggest you contact a personal injury attorney for a consultation.
The information provided is for general informational purposes only and is not intended to be legal advice. I am only licensed in the State of California and I am not providing you with specific legal advice. The law changes frequently and varies from jurisdiction to jurisdiction. Being general in nature, the information provided may not apply to any specific factual and/or legal set of circumstances and/or the jurisdiction where you reside. No attorney-client relationship is formed nor should any such relationship be implied. The information provided is of a general nature is not intended to substitute for the advice of an attorney, especially an attorney licensed in your jurisdiction. Your question, although you may believe is simple, it is not simple. You require legal advice, please consult with a competent attorney licensed to practice in your jurisdiction.
Insurance companies have been known to abuse the rights of their customers. I recommend you to speak with a lawyer. Most of us on this site offer free advice. So, there is nothing to lose and a lot to gain by contacting one of us.