Spring was shown a straight red card by referee Geoff Eltringham in the 5-1 defeat at Brisbane Road following his 14th-minute challenge on Andrew Welsh.
Orient launched an appeal against the decision and Spring's subsequent three-game ban, but Eltringham's decision has been upheld.
The former Luton and Leeds midfielder will miss Saturday's clash at Charlton and the following home games against Plymouth and Southampton.
Source: PA
Source: PA