The phrase "grind on" refers to a prolonged and tedious task or situation. There are many synonyms that can be used to describe this, including dragging on, plodding, enduring, persisting and trudging. Other words that could be used include persevering, soldiering on, and bearing up. The phrase can also be used to refer to someone who is grinding away at a task, such as working hard or pursuing a goal with determination. Some synonyms for this could include striving, persevering, and applying oneself diligently. Regardless of the context in which the phrase is used, it generally connotes a sense of challenge, endurance, and hard work.