According to the dictionary:
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keep (CONTINUE DOING)
to continue doing something without stopping, or to do it repeatedly
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And the sentence that is given with this construction as an example:
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I kept hoping that he'd phone me.
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So... it seems such a usage of "kept" is possible, in the meaning that somebody didn't stop doing something, which is equal to the meaning that somebody continued doing something.
There is also a construction “keep on doing something”, which is a phrasal verb. Its meaning is: “to continue to do something, or to do something again and again”. The example sentence is: “She kept on asking me questions the whole time.” The meaning of both constructions seems to be the same or very very similar.
In conclusion, your sentence is correct.
