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Matus, I look forward to answers to your query as I have a similar problem with one of my Kollsman periscopic bubblw sextant.  For quite a while (about two years after I purchased it) it was giving a fairly consistent required IC.  This was across all manner of temperature and humidity and hundreds of individual sights.  Then, one day, it started to give ICs that were different for rising objects and falling objects but were fairly constant.  Until a little while ago it started to give variable IC.  As with your A-12, the IC was fairly consistent for the sight series but would change day to day over about 5' range.  Like you, I use a tripod but I am always outdoors.

One thing that I do as part of my sight reduction is evaluate the number that comes out of the averager vs the final index reading +/- the expected rise/fall of the object.  It is not a perfect method of evaluating the "goodness" of a sight (eg: if i don't center the object in the bubble perfectly, but consistently have it tracking off center) but it's a good way to tell if I was at least paying attention. There is a rise/fall rate table in the Air Almanac or Pub249, I forget which, that can give you that expected rise/fall rate.  I use a Polhemus whiz wheel to get this information.  I also use the full 2 minute run of the averager.