Will low readings of CYA cause your pool to have low chlorine even if you have added the recommended dosage?

It may, actually. I have been working at a pool supply store for the summer and can tell you that having low CYA can make you go though chlorine like crazy, since it is the CYA that keeps your chlorine levels stable. It should be between 40 and 125 if I remember my numbers correctly. Have you had any other problems, such as phosphates? Phosphates eat up chlorine like crazy, though the problem would need to be tested for by a pool water tester.