Genya, I am jealous- living in a colder climate with nothing so romantic looking like the Danube during a summertime evening.
Can provide you some pointers. First if you get a chance, check out the youtube video "Life Cycle of a Lithium battery pack, how many cycles should it last?" And basic Li Ion short videos. Then the Apple battery website may give you additional ideas how the potency has gone up for laptops, from 300 to 1000 cycles, and operating parameters:
Determining battery cycle count for Mac notebooks - Apple Support
http://www.apple.com/batteries/maximizing-performance/
By now, you know that it all boils down to how those Electrons travel through the circuit, and Lithium Ions go back to the positive cathode. A car analogy would be the fuel line and fuel pump. If a car's engine just shuts down, it is far more likely that the causes could be fuel line leak, dry tank or fuel pump long before the ECU computer having a code error. You have to trust honest feedback experience that I did try in the past 3d party batteries numerous times. Am allergic to them as, dubious quality or source, they could last from a few weeks to just a few cycles. Wasted time and money, often unable to return them as, when defective, they are classified as dangerous goods. The Li liquid inside, if not produced under stringent QC, is never going to work predictably. A few hours of ambient air overexposure can fail them during assembly - is happened even to the 6S recall. And any shutdown like you re experiencing suggest that, in the lower Depth of Discharge (sub 30%), your particular battery cannot deliver those electrons. Fuel is cut off. You are also welcome to go read 3d party reviews on Amazon, some are really bad, 30-50% failure in weeks. As the video explains, the module controller is another key part- and Apple's modules tend to be very good and meant to work and calibrate with Apple's own firmware. Once you introduce non-OEM of questionable quality, no technician on the planet can guarantee a long term working battery. And the fact that your got 2 years of the previous one, amazing but not the norm.
So am not trying to convince you to spend money, just that, technically speaking, I would never have expected your non-OEM battery to work more than a dozen to a few hundred cycles. And, as all those here whom replaced them resolved it, am quite confident that where you to do so, it will work for you. I still recommend an Apple Authorized Serivce center, via https://locate.apple.com/hu/en/service/?pt=3&lat=47.5&lon=19.0833333&address=Bud apest&carrier=T-Mobile
If this does not work, welcome to come back and call me names. But am very confident it will work and, in your case, it is not iOS related even if it appears so.