Answered by Shaykh Faraz Rabbani
What if one intends to fast an optional fast at night before going to bed and then the next morning oversleeps and wakes up for fajr but misses suhoor.
1- Can one decide at this point (after fajr has come in) not to fast for the day or would they be breaking their fast if they decided not to fast at that point?
2- Similarly, can one refrain from making an intention to fast for fear that they will not want to fast in the morning and just wait until morning, even if it is after fajr, to make their intention?
Walaikum assalam wa rahmatullah,
 It is permitted to break a voluntary (not obligatory) fast with an general excuse, such as when one didn’t manage to wake up for suhur.
 It is valid to make intention for both current (not make up) obligatory fasts and also voluntary fasts even after Fajr time, up to the mid-day, provided that one did nothing that would invalidate the fast any time from Fajr time.
For details, see:
THE INTENTION (Intention)
The intention of fasting is necessary. If a person stays away from all those things that break one’s fast without an intention, the fast will not be valid.
It is not necessary to express the intention verbally as intention simply means to intend. Thus, the firm determination of the heart will suffice. However, it is better to express the intention verbally also: Bi sawmi ghadin nawaytu (‘And I intend to fast tomorrow’)
The time for intention lasts up to midday for specifically obligatory, specifically necessary, sunna and recommended fasts. This is mid-way between the beginning of fajr time to sunset (the beginning of maghrib time).
The intention for non-specifically obligatory and non-specifically necessary fasts must be made before the beginning of fajr time.
[F: The time for intention starts from Maghrib time of the night before.]
And Allah alone gives success.