Thanks for the explanations. based on your comments, I believe that it would be important to establish a long-term experiment to achieve the final answer for this thread.
I believe that 1.8V is the manufacturer limit and therefore it is too critical for normal operations. Therefore, I would like to establish 2V as a "secure/reliable" limit. I am following now the datasheet and using a 2MHz clock to realize the use of this voltage. The main question is, under these conditions, do we have a secure/reliable operation of the ATmega328P chip with 2V?
To answer this question, I will create the following testbed and proceed as follows:
1) Testbed with 2 distinct boards/chips:
1.1) Board#1 will run ADC tests, math calculations, timer, and 9600bps serial communication operations.
1.2) Board#2 will run the same app as #1 plus write/read Flash operations.
2) External 2.0V power supply for each board.
3) 24h-test with external logging via serial interface to a PC.
If the results are successful (no interruption in a sequence of numbers with timestamp), my final intention is to create my own BOD scheme with one ADC channel which will check the battery voltage. The trigger will occur when the battery goes equal or below 2V.
I cannot use BOD because I MUST LOG the bad battery status (it is an application requirement) and not only allow an automatic RESET operation provided by BOD.
In this way, when the battery goes equal or below 2.0V (frequently checked), my program will save/log this fact at the Flash and will enter in an endless loop. I have already an external watchdog hardware which, when not regularly "refreshed" by the main program, will cause a continuous RESET of the MCU. This will occur after some seconds following the low battery detection. Therefore, no Flash corruption will occur from that point on. I believe that this design is enough for my needs.
Any additional ideas/comments are welcome guys!!