Needs to be jumped every time

This car has many issues. We replaced the transmission in March with a rebuilt one we also replaced the plugs and wires at around the same time. Soon after that we were having trouble with it starting on occasion and it has been diagnosed as a fuel pump going bad. We have to turn the key to on 5 or 6 times in order to prime the pump. Then it may start or it may take a second cranking of the engine for it to start. Now, it has gotten to where the battery will try to crank it a few times before you hear the starter clicking. At first this was happening overnight. We would jump the car and it would be fine getting me to and from work but the last few times I drove it, it had to be jumped every time I try to start it. I've taken the car back to different auto parts stores to have the battery checked and they all find that the battery needs to be charged but otherwise tests as good and the alternator and starter are both testing good. Even after driving the car for an hour before parking it, I had to get a jump start in the morning. I've made sure that the radio, lights and A/C are all off before shutting off the car.
I understand the issues with the fuel pump but don't understand what is happening to the battery. Could priming the fuel pump really be draining the battery that much?