Typical motif in case of hydrogen bonds is charge transfer from electron rich acceptor Y to (usually) anti-bonding X-H σ* orbital. If so, the X-H bonding distance increases, bond weakens, stretching frequency decreases. In IR spectrum, it is visible as red shift of X-H peak and that particular peak intensifies.
Usually the peak intensity has to do with the amount of bonds it represents in the studied material.
Why does peak intensify in this case since it represents the same X-H bond, and the number of bonds is unchanged? I would've guessed it would, on contrary, decrease, since proton exchange between X and Y may occur and sometimes X-H...Y would become X...H-Y. What am I missunderstanding here?