You will not lose your disability benefits just because you move from one state to another state. This means you do not have to re-apply for SSDI or SSI if you move within the U.S.
If you are moving out of state or even within the state, it is important to notify the SSA of your change of address. This can be done conveniently online. The sooner the SSA is notified of this change, the less likely you are to have issues with your disability payments or miss out on other vital correspondence.
If you are receiving state supplemental payments, you must also notify the appropriate state agency of your move. Otherwise, you may face penalties like those issued by the SSA.