Some great advice above, I would add, if you have the ability to open the cover for the reader, or share a photo/ make / model of the reader, somebody here may have some experience with that particular reader.
As far as what you have experienced so far, to me, it sounds like a coupling / read range issue, that you may be able to refine / improve with a couple of tweaks.
As mentioned above, the xFD with help you picture where the antenna is, and you can use that to your advantage.
The one you are getting a beep on, have you tried moving slowly, with a swiping action across the face
