Maybe I am not describing this correctly because I already received a reply that the batteries you mention are for the Nest Protect, not Detect. I don't know what they are called but I am talking about the small device on the door that detects motion. I replaced them with the batteries recommended in the Nest manual.
I'm seeing the same problem! 11 days after relaxing the batteries (with the recommended Energizer Lithium batteries), I'm seeing that the Nest Protect is showing a low battery again. The first set of batteries lasted almost a year. This second lot, 11 days. The original batteries are still going strong in the second Nest Protect I have at home. Also nearly a year old.