Something is wrong if you only got 4 days, unless you had hundreds of videos.
Maybe you did receive bad batteries, but that would be surprising. They have a long shelf life, very long, so they shouldn’t have discharged by any amount before deployment, and they are a good quality make.
It should have come with two energiser lithium ultimate. Definitely worth getting a new set of those before doing more testing, but if they go too, then you have a fault. We have read about hot cameras a number of times, so it’s not totally unheard of.
Is the camera warm to the touch? What is the temperature reading for the camera in the app? If it isn’t faulty, it takes ‘some going’ to drain the batteries in a few days. If they go in a few days again, then you should raise a support ticket, unless you have a huge amount of recordings, or viewed live for a whole heap of time.
One user, Joel_Ek, reported that his wife drained a set in a few hours, if I recall correctly, by clearing snow off their deck, without having disarmed the camera. This would have produced a lot of consecutive recordings, so not unexpected.
As I reported earlier in this thread, my experience is that they last exactly as Blink describe. 6 months at 4 to 5 times their specified rate of use. At least 12 months at double the ‘normal’ rate of use, and I’m hoping for longer still, for one camera, where my usage is much lower than normal, very much lower. Currently at a year and counting, and all remains well.