If you really want to save a replay, write down the game number (not the match number) during the game. Afterwards, if you see the replay has not been saved, in Windows navigate to %AppData%\Wizards of the Coast\Magic Online\3.0 and locate the file titled {username}.mygames, where {username} is your mtgo username. Open that file in a text editor and place your cursor at the end of the file. On a new line, add information in this fashion:

{game number}#{match number}#{date}#{time}#{format}#{player 1}#{player 2}

The game number is the only important information, the rest can all be junk as those are just for display purposes. Save the file, then go to the mtgo client and watch a different replay. The Games list should then update with the added game at the top.

Source: MTG Salvation