"continue writing" is a correct and usable phrase in written English. You can use it as a way to emphasize that someone should continue with their writing task. For example, you could say, "You should continue writing while I finish up here.".
But I was unable to continue writing.
How long will he continue writing it?
Throughout this time, they continue writing letters.
I always intended to continue writing and I still do.
Nonetheless, the compulsion to continue writing into the darkness must be strong.
And all businesses will be able to continue writing off the investments they make in 2012.
During this time, he received a letter from his English publisher urging him to continue writing.
Awesome tool! I started using it one year ago and I never had to look for another app
Ha Thuy Vy
MA of Applied Linguistic, Maquarie University, Australia