What is the ruling on the vow made by the questioner to fast on the day she misses Fajr prayer, and does this vow fall under the dispraised category of vows mentioned in the Hadith: "Indeed, it does not bring about good, but rather, it is used to extract from the miserly"? And what is the solution to the problem of continuously missing Fajr prayer despite attempts?

If you have made every effort to wake up for Fajr prayer, there is no blame upon you, but do not despair of trying again.

As for the vow you mentioned in your prostration, if you uttered it verbally and it was not merely an inner thought, then it is a vow of obstinacy and anger (nadhir al-lajaj wal-ghadab). Its ruling is like that of an oath, and its maker has the choice between fulfilling it or breaking it, in which case an expiation for an oath (kaffarat yamin) becomes obligatory upon him.

However, if it was merely an inner thought and intention without verbal utterance, then nothing is binding upon you.

We also note that the preponderant opinion is that making vows is disliked (makrooh), even though fulfilling them is obligatory.