month after month; with each passing month
Set phrase emphasizing gradual change or accumulation over successive months. Often used in written or slightly formal contexts.
Month after month, his Japanese improved.
Sales are increasing with each passing month.
A set phrase combining 月 (month), を (object marker), 追う (to follow/chase), and ごとに (each time). Literally 'each time one follows the month', it has become a fixed expression for 'month after month'.