According to Maryland laws (especially MD code section 19-508) there is a 12 month statute of limitations in which to make a claim. Specifically it says that in subsection (2)(i) that a policy may set a period of not less than 12 months after the date of the motor vehicle accident within which the original claim for benefits [PIP] must be filed with the insurer.
Section (b)(1) goes on to state that when an insurer that provides the benefits receives written notice from an insured of the occurrence of a motor vehicle accident for which benefits may be available, the insurer shall notify the insured by mail of the latest date on which a claim may be filed for benefits. So the insurance company should notify you on how long you have to make a claim.
Many Maryland lawyers state that the statute of limitations in most MD personal injury cases is three years in total. However if you are asking how long the claim can stay open once it has been made, usually it should be taken care of in a reasonable amount of time. Section 19-508 (a)(1) says an insurer shall make all payments of the benefits described in 19-505 [personal injury protection coverage section of MD law] of this subtitle periodically as claims for the benefits arise and within 30 days after the insurer receives satisfactory proof of claim.
MD Code section 19-511 gives more information on settlement procedures if you would like to read more yourself to see about specifics that may help you in your situation. You may instead want to speak with a lawyer about specific statute of limitations that Maryland has for medical claims arising from an auto accident or get consumer help on this issue from the Maryland insurance regulator.