This would likely only happen with out of date files. Make sure you delete everything and redownload from scratch, including the base game, beyond the bet and the nsfw patch.
Viewing post in A Date with Death - Beyond the Bet DLC comments
I've done that twice now (my poor laptop) and both times i go to my saved file after the NSFW scene, played through diolague, and it still kicks me back to the start screen. Theres also a glitch file that keeps adding itself back into the game folder, even after i delete it. Is it the old dlc? Ive checked lord knows how many times to make sure things were in the right folders and I had the right files. (sobbing rn) While if i click on the Sleep for the Night option instad of the NSFW scene, it works??? Maybe im stupid