Arduino Pro Mini lower BOD problem
When you go below (or above) the manufacturer's voltage/clock specifications, expect some problems. One chip may work another will not.  Remember the lower the voltage normally the slower the clock needs to be.  The CPUs are cut from a wafer (size and geometry specific) which may contain many thousand CPU die, they are at different locations on the wafer they will be a little different and they make more then one wafer.

Check the data sheet, it will show what clock speed will work at what voltage.  As the CPU clock changes so will your baud rate so plan on recalculating that if you change the clock. Example:  If you are operating with a 16MHz clock and change it to 8MHz the baud will be exactly 1/2.  If at 9600 it will be 4800 unless you modify the clock dividers.

Your error indicates a potential baud rate problem. One of the funny things that happens when the voltage is above/below the manufacturer's speck not all instructions operate properly over temperature. Clock problems should be expected.