For a year after my father-in-law died, my wife kept an electric memorial light plugged in. Now the year is over. The 11-month ceremony has come and gone, and the 12-month ceremony has come and gone. My wife wonders whether it is now compulsory to unplug the memorial light, or whether she is permitted to leave it burning if she prefers.
There is no minhag that requires or suggests keeping a memorial candle lit for more than twelve months- not at home and not in the synagogue. It is forbidden to mourn more than what is prescribed by the halacha and by Jewish custom. You might suggest that your wife continue to honor her father's memory through additional good deeds- tzedaka, tehillim etc.