Is it permissible to break one’s fast while traveling a distance of 60 km, given the extreme fatigue from travel, when one has vowed to fast for a consecutive month, and would this affect the continuity of the fasting?

The mentioned distance does not reach the limit for shortening prayers (qasr). Therefore, breaking the fast during it severs the continuity of the fasting. Even in a journey qualifying for qasr, there is a disagreement among scholars as to whether it breaks continuity or not. For this reason, the questioner must continue her consecutive fasting until she completes the fasting of the month she vowed, as that is easier for her than resuming the fasting of another month.