Is "a month" not the direct object in this sentence? And if it is, should it not be "ένα μήνα"?
Month is a masculine noun, and the indefinite article for a singular masculine noun is ένας. 'Ενα is the indefinite article for a singular neuter noun and μια is the indefinite article for a singular feminine noun. In the example, you can look at the ending of the noun to determine the gender. I may not recall all of the rules, but it is something like : Masculine nouns end in ος, ας, ης Neuter nouns end in ο, ι, μα Female nouns end in α, η
So μήνας is a male noun and thus should use the indefinite article 'ενας.
To add to Diana's comment, μήνας here is not a direct object, it's a predicate. So it's in nominative, not in accusative. Είμαι ένας άντρας (nominative) and not είμαι έναν άντρα (accusative).