persist with (something)
To continue with some pursuit or activity with steadfast or obstinate tenacity. The union persisted with its demands for better pay and benefits, threatening to extend the strike until they were met. I'm not sure why he persists with this career as a musician when he's clearly nowhere close to being successful.
persist with something
to continue the state of something; to extend an action or state. Please do not persist with your demands that I agree to your terms. If you persist with this intrusion, I'm going to call the police.