is there something that a patient can do after being misdiagnosed on two separate occasions by the sme hospital

If you sustained an injury or worsening, exacerbation of your medical condition due to the misdiagnosis, you would have a claim against the hospital.  If there wasn't an injury, worsening, exacerbation of your medical condition due to the misdiagnosis, then you would not have a claim against the hospital.
Medical malpractice is negligence.  Negligence on the part of the hospital is the failure to exercise due care (that degree of care that a reasonable hospital would have exercised under the same or similar circumstances to prevent foreseeable harm).  
Assuming you have a malpractice claim against the hospital, prior to filing a lawsuit for negligence against the hospital, it may be possible to settle the case with the hospital's malpractice insurance carrier.  When you complete your medical treatment and are released by the doctor, obtain your medical bills, medical reports, and documentation of wage loss.  Your claim filed with the hospital's malpractice insurance carrier should include those items.
Compensation for the medical bills is straight reimbursement.  The medical reports will document the nature and extent of your medical condition and will be used to determine compensation for pain and suffering, which is an amount in addition to the medical bills.  Compensation for wage loss is straight reimbursement.
If the case is settled with the hospital's malpractice insurance carrier, NO lawsuit is filed.
If you are dissatisfied with settlement offers from that insurance carrier, reject the settlement offers and file a lawsuit for negligence against the hospital.
If the case is NOT settled, your lawsuit against the hospital must be filed prior to the expiration of the applicable statute of limitations or you will lose your rights forever in the matter.
 

If the misdiagnosis--
1) Was unreasonable, so that a competent medical care giver would not have made it; and
2) Led to you suffering some significant injury or harm, and/or significant out-of-pocket economic losses or costs, like large medical bills not paid by insurance (or Medicare/caid) or lost wages
--you may have a viable malpractice case. You need both elements for a viable case: liability based on a negligent or careless diagnosis; and damages or injuries resulting from that misdiagnosis. 
Remember that not all doctor errors are malpractice--only ones which were unreasonable, since the law accepts that doctors are not perfect and cannot be held to a standard of perfection; they only have to do what a reasonable doctor would do. So if the diagnosis, even if ultimately wrong, was a reasonable one which a doctor could make based on the evidence, symptoms, any test results, etc., the doctor did nothing wrong.
Note also that medical malpractice cases can be very expensive, since you *must* have a medical expert examine you, write a report, and testify as to the carelessness and its effect--you, as a layperson, are not compettent to testify as to whether  diagnosis was unreasonable or not, or what its effects were. But such experts can be very expensive, so unless  you suffered significant injury *because of* the misdiagnosis (e.g. injury that would not have occured anyway) or large costs due to the misdiagnosis, there is no point in suing.