I saw this post and it describes my situation exactly (for some reason I couldn't reply so starting a new inquiry)
I have 3 Nest protect units around the house and I only experience the quick drain on batteries in one of the units. I am using Energizer batteries. I see there's a recommended battery which I am happy to try but suspect it won't make a difference given the other two units are lasting well over a year. The problem unit has had new batteries in 2021 on Mar 15, May 12, July 11, Sept 15 and I just got a warning this morning Oct 14) that I should replace them soon. I don't mind replacing batteries every year or so, but every 2 months is expensive.