I bought my Camry Hybrid new in May 2014. The first 9 months the car started with no problem. I went away for 3 weeks and came back to a car with a dead battery. After charging it I began to have problems starting the car. The ready light would not come on or would only come on after waiting 4-5 minutes and turning off the radio, fan and lights. The problem has happened when the Aux Battery was 82% charged. I can attach jumpers to an emergency battery to jump start it. I now have to charge the battery weekly. The Toyota dealer told me that the car is not completely off when you turn it off. He said the various electronic devices are on and draining the battery. He claims this is how the car was designed and completely normal. He told me this while the car was still under warranty.
I can understand the keyless entry system being on, but I doubt that it should be a big drain on a car battery. The battery has enough charge to start the engine, but for some reason something is keeping the ready light from coming on and allowing the car to start.