Based only on my experience.
Internet shutdown will prevent on-going & future saving resulting in a failure until you get back online. Sometimes it forces me close the engine. Easily one of the greatest downsides of Construct 3 is being unable to save your game locally without internet connection. That's just silly. Definetely not the type of engine you should take to some distant quiet village to work with.
If your PC suddenly turns off during the saving process then there is a very high chance that your save will be corrupted and there is nothing you can do about it. Make backups as often as you can. Losing one day of work isn't as painful as losing one month.