Endless time is available with the Patreon Exclusive version, which also comes with cheats and selectable outcomes for various scenarios.
There's a few reasons why the game has limited time:
-Stuck in Sutton is my first game and I wanted to make something I could realistically complete
-Story events get messed up if the same day repeats
-The time pressure is a part of the premise. It's supposed to feel like you have to do certain things (Stripping and Prostitution) to have a chance of leaving Sutton.