1st thing you should do is remove the batteries and use a digital meter to find out what the actual battery voltage is. My new ones measure at 1.8 Vdc. When they are dead, they measure at 1.3 and typically, only one battery is dead. The other is at 1.5 or higher. So now you know if battery is actually still good or not.
Next up, is the Blink camera giving false readings? Is the Blink camera killing the battery early? A sure way to tell is if the camera is warm or hot, you have a bad camera. It’s drawing too much current and heating up thus killing batteries.
In any case, the 2 year or more like it “up to” 2 year battery life is well documented in this community forum, facebook,twitter, and youtube. Myself, I have 6 original XT cameras. 1 of them actually lasted 2 years on original batteries. How? It has less than 40,000 seconds of use. How you want to split up 40,000 seconds is up to you. Do the MATH!!! It is 11.111 hours of video over two years. Very easy to burn up 11 hours of video and live view in way less than 2 years.
For the math wizards, 40,000 seconds = 666.666 minutes. That’s beast mode for Blink. LMAO