All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.
Fulfilling a vow is one of the acts which draws a person closer to Allah, yet it is not obligatory, but if you bound your intention with it, then you are obliged to fulfill since Allah, The Exalted Said (What means): ”Let them perform their vows.” [Al-Hajj/29]. In addition, the Prophet (PBUH) said (What ): ”Whoever vows to obey Allah, let him obey Him. Whoever vows to disobey Allah, let him not disobey Him." [Related by Al-Bukhary].
Therefore, whoever took a vow to fast for one consecutive month is obliged to fulfill it literally and if he missed a day within this month is obliged to fast the whole month consecutively once again.
In this regard, Al-Imam An-Nawawi (May Allah have mercy on his soul) said: ”Taking a vow to fast an entire month is to be considered according to the form of the vow: there are two opinions on taking a vow to fast a consecutive month and the most preponderant one is that a person is obliged to fast the entire month once again consecutively in case he broke a fast within it and the same applies if he missed the whole month.” [Al-Iqnaa’ vol. 1 pp.390].
In conclusion, you (Questioner) are obliged to fast a new consecutive month and you are free to choose the easiest month for fasting. And Allah knows best.