Has the vow been accepted, or must I repeat fasting the ten days, if I vowed to fast ten consecutive days, then broke my fast one day due to extreme fatigue while traveling for Umrah, and then completed the fasting thereafter?

A Muslim should not hasten to make a vow (nadhr), because he might become unable to fulfill it and thus fall into sin. Scholars have differed on interrupting the continuous fasting of a vow due to an excuse. The preponderant opinion is that anything for which breaking the fast is permissible in Ramadan does not interrupt the continuity of the fasting, such as travel, illness, and menstruation. If a person breaks the fast due to a legitimate Shar'i excuse, he builds upon what he has already fasted, and he is not required to restart from the beginning. However, if the period between the cessation of the excuse and the completion of the fasting is prolonged, then the continuity is broken, and he is required to restart.