Sumerian religion and language surviving in some form or another is possible but very difficult. Sumerians will have to adopt papyrus and parchment, as their clay tablets make the administration of their religion and political systems extremely difficult when you have oral or papyrus-based religions like Zoroastrianism, Hellenism and Christianity that are easier to propagate and control, and they also somehow need to not get steamrolled by the Medes and the Greeks, which is the moment when Sumerian culture really starts to disappear once and for all as the Sumerian script starts getting replaced with Phoenician and Syro-Arabic alphabets, the Sumerian liturgical language starts getting supplanted by Avestan and Greek, and Greek and Iranian gods start assimilating Sumerian deities.
The second Babylonian empire allying itself with Greek city-states and Egypt against the Persian-Median offensive is probably the best way to have Sumerian culture survive. Then they need to start checking the power of the expansionist Greeks as well. And then they need to make cultural adaptations like religious reforms that don't make temples and clay tablets the only repository of sacred knowledge and start adopting the superior papyrus and parchment of Egypt and the Levant so that religious texts are more easily propagated and a more cohesive and stronger religious canon arises.