When do I lose 2 SO Points at the end of each day?
You deduct the SO points from the Artillery Unit after you've collected your daily SO points.

In the rules on page 21, the order in which actions happen during the End of Day phase are pretty specific:


  End of Day
  
  
  No Fly Stress Recovery
  Gain Special Option Points
  Move Enemy Battalions
  Lose Special Option Points (Map)
  ...
  


During the End of Day, you gain your daily SO points before losing any because of your current map configuration. This includes any points lost through unit effects. This is confirmed by user Walter Gagajewski on Board Game Geek, where he outlines a play session:


  I gained 5 SO for 6 total and lost 3 for the Command units at full strength, 2 for a unit effect, and 1 for a unit in Friendly Rear.


His notation seems to be slightly out of order, showing SO gains and loses after the start of the next day, but his play flows in the same order as the rules indicate. The loss from a unit he is referencing in the above quote is from the Artillery Unit (1S), so that helps to verify how the Artillery Unit functions.



Full disclosure: I have never played the game, but I've just spent a significant portion of my life reading the rulebook and searching the internet for player logs of game sessions.