to keep up (with someone/something)

"He started to walk faster and the children had to run to keep up."
"Wages are failing to keep up with inflation."
"You'll have to walk faster if you want to keep up."

to keep up

"I read the papers to keep up with what's happening in the outside world."
"Old people find it very difficult to keep up with the changes in society."

to keep something up

"You must eat to keep your strength up."

to keep (something) up

"Keep up the good work!"
"You're doing very well everybody. Keep it up!"