persist with

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.
See also: persist
Farlex Dictionary of Idioms.

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.
See also: persist
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs.
See also:
  • persist with (something)
  • persist in (doing something)
  • persist in doing
  • in pursuit of
  • in pursuit of (someone or something)
  • be in pursuit
  • pursuit
  • be in pursuit of (someone or something)
  • honeymoon phase
  • honeymoon stage
References in periodicals archive
Experts have predicted the prevailing weather condition would persist with even more intensity during the next few days.
While incisional pain can persist with any patient, it is more common among younger patients, women and patients who may have had deep infections near the incisions.
THE FA will persist with 5.15pm kick-off times for the FA Cup final despite criticism it finishes too late for fans in the north to catch the last trains home.
And FA general secretary Alex Horne added: "I'm not surprised that fans want to be able to support their teams and travel but on balance we have said clearly that we think 5.15pm is the right kick off time for the final and we want to persist with that.
Although most individuals with allergies to foods in this latter group tend to persist with these allergies indefinitely, some children will develop tolerance to these foods and will be able to reintroduce them safely into their diet.