I often come across sentences like these
He kept on chasing the thief even it's deep into the night.
Shall we keep practicing in the next few days?
But as far as I'm concerned, both of the following sounds fairly OK.
He kept chasing the thief ...
Shall we keep on practicing ...?
I can barely remember that they have a monir difference in meaning but I Googled (and searched ELL.SE) around and found only usage differences. Can anyone tell the exact difference in meaning?