<p>is it:
They began to circle once more</p>
<p>OR</p>
<p>they began circling once more</p>
<p>is it:
They began to circle once more</p>
<p>OR</p>
<p>they began circling once more</p>
<p>the first one because “once more” implies an instant. there is no continuous action implied by a gerund</p>