Every LED in each vertical column is connected together by a printed copper trace, on the back side of the Peggy 2LE circuit board, that runs along each row and connects the “round” hole of each LED together.
(The “square” holes connect every LED in a horizontal row, on the front side of the circuit board.) 

 So, it appears that you have some broken traces on the circuit board. Either the circuit board was scratched in those three places where the column turns off, or the trace was somehow otherwise damaged.

The good news is that it isn’t so hard to fix. 

Identify, on the back side, the three exact places where you have breaks– in those three columns between the working LEDs and non-lit LEDs. In each of those three places, solder a short wire (e.g., a piece of clipped resistor lead or LED lead) between the pin of the lower (working) LED– the pin in the round hole! — to the pin of the upper (non-lit) LED– again, the pin with the round hole.

Fix one at a time; make sure that the fix works on the first of these locations before going on to the next. 

 Good luck, and please let us know how it goes. :)