When it comes to expressing the act of persistent continuation, there are a multitude of synonyms for the phrase "keeps on." Some common alternatives include "perseveres," "endures," "maintains," "sustains," "pursues," and "carries on." Each of these terms carries a slightly different connotation and may be more fitting for specific contexts. For example, "perseveres" suggests a continued effort in the face of obstacles or challenges, while "carries on" implies a more steady, consistent progression. By utilizing a variety of synonyms for "keeps on," you can add nuance and variety to your writing and ensure that your meaning is clear and precise.