A single word that means "to push yourself"

You could use "disciplined":

A controlled behaviour; self-control

Someone who is disciplined won't easily let himself back out.

strive - make great efforts to achieve or obtain something

persevere - continue in a course of action, in the face of difficulty, or with little chance of success

The choice mainly depends on whether you want to emphasise the difficulty or the continuing, but it's important to note that unless the context clearly rules it out, there's a risk of perseverance carrying those overtones of potentially futile effort.

Perseverance comes to mind....

Persist - you'll eventually find it worthwhile.