@skywatch Thank you very much! Your advice helped. Not shure what it was on BOTH devices - my mistake or some corruption of fuses/program.
On first device (where i found problem) - there were different fuse bits (but according to my eyes BOD was even disabed, but not shure). On the second (where i tested) fuses were checked and were correct. I tried to play with fuses and erase chip... and something strange happened - or chip memory was broken or i can't verify program when box "erase flash and eeprom" is checked... so i took fresh nano, programmed it and resoldered MCU into the second device.
So both devices now are fixed and tested - both work till ~1.9V.
Thanks, you saved my brains!

Today i suddenly find out, that Tekka updated app. Old app said "there is an update" and i've clicked link, which lead me to dropbox page.
So anyone, who previously blocked all traffic for program (@iguaan , @nfj25 , @Mac65 , @tplet) - you may want unblock it in your firewall and update.
I just replaced MYSController.exe and MYSController.ini files, leaving all other - it worked! Did not yet tested all functionality. But still make backup of all files for sure before dong that. Also you may need click on sensor and choose "settings->offline FOTA update" in order OTA to work. I'm wondering what does "online" version mean...
Thank you very much, Tekka!