Making a wrong a right
 

1 out - R1 on 3rd, R2 on 1st.

Fly ball blooper between SS and LF caught by the SS. R1 tags up from 3rd and is safe at home but R2 fails to tag up and is called out at 1st for the 3rd out.

The umpires have a brain cramp and do not count the run. The call is accepted by both teams.

Two innings later they realize their mistake and count the run. Can this be done? Correctable error?

I dont see why not, is basically just a score keeping correction.

Sure, fix it. If they can fix this same thing in Major League Baseball, why not in softball? :rolleyes:

(From 2007) "Time Plays" can cause confusion among players, managers and occasionally umpires | Baseball Digest

You would 'correct' this after a subsequent pitch (legal or illegal) has been thrown? (let alone two innings later)

what would you do if one of the teams wanted to 'replay' those two innings because their stratagy would have been different had the score been different. ;)

Hate to use MLB examples in FB, but, quite often the Official Scorekeeper will change what was originally recorded in the game and fix it.

A recent example was in the 11th game of Dan Uggla's 34-game hitting streak, where a play was recorded as an error. 24 hours later, they changed it to a hit.

Whereas this could be a protestable error (incorrect application of a rule), why wouldn't it be wise to simply fix it upon discovery?

The argument against changing it is that in general you can't go back and fix anything. If for example, the umpire judged that the appeal occurred before the runner got home, the run certainly wouldn't count and no one would say that the umpire can go back and change his mind.
The argument in favor is that no ruling is actually made here and it's simply a scorekeeping error.
I don't know that the book says anything about this, but I'm not sure how you can take the latter position without saying that it can be fixed the next day, or the next year, or forever.

The rule application isn't protestable after a next pitch, so that isn't a factor. The issue is if this is a scorekeeping error or a ruling that can't be changed. Okay, they asked the umpire, but the official scorekeeper could STILL have a different score in the book and on the board, because it really isn't the umpire's call, unless the umpire states the out was made before the run scored.

I am aware of game scores that HAVE been changed after the fact, when it was determined a scorekeeping error was the sole factor.

Whether or not the runner crossed the plate before the 3rd out is the umpires call - and is final and unprotestable.

However, what the score is, is not the umpire's decision. The score is what the score is. The runner scored regardless of how many innings went by before it was put on the scoreboard or in the scorebook correctly.