As of November 2013 there were 17 characters that were introduced at one point into the game, but were limited-time. Meaning, if you didn’t purchase/earn them during the event you won’t be able to get them ever (unless EA re-releases them).
All characters listed below are no longer available. Click on the character for more details.
Talking Krusty Doll
Valentine’s Day 2013
St. Patrick’s Day 2013
Wacking Day 2013
4th of July 2013
Suzanne the Witch
Items from Halloween 2012 (except for the Mayan God) returned in 2013
Tribal Indian Chief
The Yes Guy
Plow King (Skin for Barney)
Mr. Plow (Skin for Homer, Returning from 2012)
Santa Flanders (Skin for Ned)
Ebenezer Burns (Skin for Mr. Burns)
Married to the Blob Episode Tie-In