Unfortunately, Mission Replay will not be available in Saints Row: The Third, through either a patch or DLC. There were a few reasons this was removed after SR2, due in part to the new game engine, some game-breaking glitches/exploits that had been available to SR2 players, and other reasons related to specific development concerns. We also hoped players would want to play through the entire game multiple times to either try out the multiple branching stroylines / choices, or to experience the entire game in another fashion be it through a different voice, character, or upgrade options.
While I know the following solution is not ideal, if you wish to replay a certain mission, you can create individual manual saves files before any major mission along the way. Yes, you're not actually replaying it with any new items you've acquired after the specific mission in question, but the potential for bringing in some of those late-game items into earlier missions presents many potential and unknown issues.
As a final point, because of your feedback here, even though it is off the table for SR:TT, the development teams moving forward are aware and this feature will be considered for any future Volition title. Please note that this is not a guarantee of it being placed into any future Volition title, but it will be discussed and evaluated by the team at large.
We all hope that you can continue to enjoy Saints Row: The Third, even without this feature.
