What is the ruling on the fast of one who doubts whether he committed masturbation while observing a fast, then experienced a legitimate excuse [that broke the fast], and Ramadan is now upon him, and he cannot make up the fast until after it?

Fasting of someone who doubts its invalidity due to using an invalidating act is sound, because the default is the validity of the fast, and certainty is not removed by mere doubt. Therefore, as long as you doubt practicing masturbation and are not certain, your fast is sound, and you are absolved of liability for that day, and you are not required to fast it again.