persevere with (something)
To continue trying to improve at or succeed in doing something. Your writing isn't going to be amazing when you first start—you have to persevere with it. Even though I struggled at times, I persevered with my studies and ended up graduating with a 3.5 GPA.
persevere with something
to continue to try to accomplish something. Do you really think it is wise to persevere with your plan? Sally persevered with her scheme to earn a million dollars.