Fasting only once per month

If you mean fasting once in every month as well as fasting the entire month of
Ramadaan, there is nothing wrong with this and this deed will be rewarded.

A man came to the Messenger of Allaah
(Peace & Blessings of Allaah be upon Him) asking him about Islam. The Messenger of
Allaah
told him to pray five times a day. The man asked, “Do I have to do any more
than that?” The Prophet
told him, “Only if you want to.” The Messenger of Allaah

told him that he had to fast the month of Ramadaan. . The man asked, “Do I have to do
any more than that?” The Prophet
told him, “Only if you want to.” The Messenger of
Allaah
told him about zakaat. . The man asked, “Do I have to do any more than that?”
The Prophet
told him, “Only if you want to.” The man went away, saying, “By
Allaah, I will do no more and no less than this.” The Messenger of Allaah
said, “He
will be successful, if he is telling the truth.” (Reported by al-Bukhaari, 2481).