I probably might check to make sure all the teeth are still in good shape on the flywheel or flexplate ring gear. Engines tend to come to rest in the same tooth area for reasons that are unknown to me.
Although once in an area of poor/no teeth it should not be able to pick up the drive again. Also quickly check the bolts on the bellhousing are not coming out. Other than that you may have got a bad replacement starter perhaps.
Not many other possibilities come to mind. Another long shot might be a flexplate with certain kinds of damage other than teeth as well. Chances are higher that you got another starter with a bad drive bendix perhaps .It can happen.