\documentclass{article}

\usepackage[
  abbreviations,
  shortcuts=abbr,
]{glossaries-extra}

\glssetcategoryattribute{abbreviation}{discardperiod}{true}
\glssetcategoryattribute{abbreviation}{retainfirstuseperiod}{true}

\newabbreviation{dr}{Dr.}{Doctor}

\begin{document}

% This is OK.
\ab{dr}. \ab{dr}.

% This is still OK.
\as{dr}.

% This period gets unduly discarded.
\al{dr}.

\end{document}