Is the fasting of one who intended to break their fast but then did not do so valid?

Your fast is valid because you did not firmly intend to break it. The default is that you are fasting, and the fast is only invalidated by a definitive intention to break it or by committing an act that invalidates it. Al-Nawawi mentioned that the madhhab is that the fast is not invalidated if the fasting person hesitates about breaking the intention or makes breaking the fast conditional on something that does not occur.