Is it possible for a Zorua line member andor Ditto to become permanently stuck in a transformation (or at least choose to stay in one)?

Choose to stay as one? Yes, absolutely. Some shapeshifters have preferred forms, and they’ll attempt to assume these forms whenever possible.

Get permanently stuck as one, however, is a different story, and the answer there is “no.” Such transformations are always conscious for the most part. There’s always something that will trigger a de-transformation, no matter how careful a ditto or zorua/zoroark is.