In informal writing an ellipsis is often used to indicate a pause in the flow of the sentence, as in this case.
The question raised is whether to repeat the (valid) use of ellipsis when the first use is no longer on page, in order to carry over the effect to the next page, or to simply use a sentence fragment on the second page.
I have not found any style guide that addresses this question, but I would say yes, repeat the ellipsis. I would liken it to using a hyphen - if you unavoidably had to hyphenate across a page-break you would hyphenate both halves to make it immediately obvious what is going on.
This is a common concern in children's books where the strategy of progressive discovery (page-level cliffhangers) often necessitate breaking a single sentence into two pages for an exciting reveal or for prompting child participation.
Given the ubiquity of this issue, review of professionally published children's books should yield real-world editor's decisions on this, but I have written and self-published a children's book, and I used two ellipses when facing this question.
If I find examples in professionally published examples, I will add them to this answer.