As I've said in my comment I think that this is a question about licensing and it usually calls for a native English speaker's ear. The best I can offer as a non-native speaker is a corpora search:
It seems that an infinitive is more common after continues than a gerund, both for "do" and "hit" as this Google Ngram shows:
Another Ngram shows that "continues" is very often followed by "to" and another one shows that in the most frequently used examples that "to" is an infinitive marker. That being said, Google is not impeccable and I haven't tested these for false positives.
As Damkerng T has noticed - whether you should use the -ing form or infinitive depends on the verb you are using (there's licensing for you - never a dull moment with it). For example I'll continue reading would be used more often than I'll continue to read. Same goes for cooking and whisking, for example.