I have been playing Pokémon Sword and I am hunting a shiny litwick through Masuda breeding and am not sure if it’s ok to close the software after saving your progress. I think I might reset my built up chances of getting shiny litwick and have to start over again
I think you're misunderstanding how Masuda Method works. Each Egg has an individual chance to be a shiny -- there are no chains, no combos, nothing that will boost an Egg's chance of being shiny. Therefore, it's perfectly fine for you to close your game -- your "built up chances" won't reset, as they never existed in the first place.
Hope I helped!