Either present simple or present continuous is fine in the context. But remember that present continuous has more immediacy: I am walking to school (right now) (but you might stop walking at any moment). "x is continuing" suggests that, right now, it is continuing, whereas "x continues" connotes a habitual way of behaving, and carries more expectation of the behaviour being continued into the future: I walk to school (usually) and shall likely continue to do so. And, of course, the use of present simple tense complements the meaning of the verb "continue", which makes present simple sound more natural
Consider students sitting an exam, and the teacher says "pens down". "You are continuing to write" means you are still writing, right now, when you shouldn't be, whereas "You continue to write...." would be the form used outside of the immediate situation, for a student who continually, or often, continues to write when they shouldn't during exams.
But this is almost an overanalysis, as, in many contexts, the choice between these tenses is a free one. In such cases, fluent speakers go "by ear", with what sounds more natural.