Since I don't have one here in front of me, my comments are going to have to be quite general.
Some baris have a "helper bar" that extends to the Bb key to help keep that key closed. If it has one of those, check to see that the adjusting screw has not been turned in too far keeping the A key from closing.
If there is nothing impeding the closing of the key like above, there is a possibility that the key has been bent. It helps to have a bright leak light to check how the key is sealing. I would use regular bottle size corks wedged under the guard to keep the Bb and B keys closed and out of the way. Then close the low A by pressing the thumb lever only. Pushing the key itself will give a false reading. If the key has been bent and one side is closing before the other, you can use a tongue depressor or craft stick under the side that closes first and gently bend the opposite side down with your fingers. If you have gone too far, then just reverse the side the stick goes in.
Very few baris can be set up so the A key closes all 3 bell keys by itself. Most commonly one must finger low Bb while adding the A key with the thumb to get the mechanics to work as it should. Posting a picture or two would be very helpful to try to diagnose the problem.