We had a similar problem due to a poor job to begin with by the contractor. In our case, the patio was at ground level. We had something called “ mud - jacking “ ( yes, I know there will be snickers about this term ) performed which lifted the side of the patio next to the house to facilitate drainage. They basically drilled a series of holes in the concrete and injected what appeared to be expanding foam that lifted one side up about 2 “.
I guess this won’t work for you if there isn’t dirt directly under the patio.
Maybe get rid of the patio and put in a deck ? $$$, I know.