"Eats into" is a common phrase used to describe something that gradually diminishes or erodes over time. However, there are several synonyms that can also be used in its place. "Erodes," "depletes," and "diminishes" all convey a similar meaning of something diminishing over time. "Consumes" and "devours" can also be used to describe something that is being slowly taken away. Additionally, "undermines," "saps," and "weakens" can be used to describe something that is gradually becoming less effective or impactful. In short, there are numerous synonyms available that can replace the phrase "eats into" and still communicate the same idea effectively.