keep on (doing something) = continue (doing something)
- We tried to calm the baby down, but he kept on crying.
- I was very tired and had a break but Mary kept on with the housework non-stop.
- He kept on talking all night!
- She kept on asking me about my ex-wife. It was rude and awkward.
- Your son kept on biting his nails in front of everyone. You should tell him to stop.
- You 've been eating all day. If you keep on like this, you will gain a lot of weight.
- Keep on working. Don 't let me interrupt you.
- I keep on forgetting to turn the lights off.
- I kept on thinking I had seen this man before.