Most people provide a trellis to train it until it starts doing it it well on its own. Does the brick surface get too hot somehow? Masonry screws might also work to help the tendrils attach.

If the brick is clean, not covered with fungus, the climbing hydrangea will usually cling very well. I think your planting location is fine. Al

The brick is very clean, no moss, fungus, or growths of any kind. The brick wall faces North/East so it gets early morning sun until about noon or 1:00 depending. Then it is in partial shade for the rest of the day until 5 or so, then full shade. So I don't think it gets very hot. I did attach a small trellis (6ft.) to get it started which it has wrapped around very well. But as soon as it reaches beyond the trellis, it can't hold on. Maybe a larger trellis? I really don't relish the idea of driving screws into the brick, and at what point would the hydrangea actually grab on for itself if it hasn't already?