Password Reset Link Not Working for Specific Users

When attempting to reset the password, some users get a reset link that looks like:

www.site.com/?ACT=11&id=yeiafcldwvej

while others get:

www.site.com/admin.php?S=0&D=cp&C=login&M=reset_password&resetcode=5P739zx4

The link with ?ACT= returns the error:

The password reset token does not appear to be valid. Please check the link you followed.

while the other link works fine. We’ve tried different user groups and different users, but this seems to be tied to a specific set of users that so far we have not been able to change. Even with deleting and re-adding the account the issue persists.