Some parishes will sponsor what they refer to as a perpetual novena, where one evening each week, there is a service of common prayer which may or may not end with Benediction of the Blessed Sacrament. These were in honour of Our Lady of the Miraculous Medal, Our Lady of Perpetual Help, Saint Anthony of Padua, Saint Jude and so forth. One made the novena by attending for nine weeks. These were more popular in years long past than today. These novena services today are sometimes done in conjunction with a daily Mass rather than as their own stand alone devotion.
I am not acquainted with any novena that is done once per month for nine months. I can only think you have in mind one of the promises of the Sacred Heart, wherein the Lord said to Saint Margaret Mary Alacoque
*12) I promise you in the excessive mercy of my Heart that my all-powerful love will grant to all those who receive Holy Communion on the First Fridays in nine consecutive months the grace of final perseverance; they shall not die in my disgrace, nor without receiving their sacraments. My divine Heart shall be their safe refuge in this last moment. *
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