First off, go to you MGSV The Phantom Pain folder, should look something like this:

C:\Program Files (x86)\Steam\SteamApps\common\MGS_TPP

Open the "master" folder and find the data1.dat file.

Now open it, go to Assets\script\lib\ and open TppStory.lua. Press ctrl+f and find " function e.CanArrivalQuietInMB(n) "

Add this after that:

gvars.str_didLostQuiet=false
TppBuddy2BlockController.SetObtainedBuddyType(BuddyType.QUIET)
TppBuddyService.UnsetDeadBuddyType(BuddyType.QUIET)
TppBuddyService.UnsetBuddyCommonFlag(BuddyCommonFlag.BUDDY_QUIET_LOST)
TppBuddyService.UnsetBuddyCommonFlag(BuddyCommonFlag.BUDDY_QUIET_HOSPITALIZE)
TppBuddyService.SetSortieBuddyType(BuddyType.QUIET)
TppBuddyService.SetFriendlyPoint(BuddyFriendlyType.QUIET,100)
TppMotherBaseManagement.RefreshQuietStatus()

And there you go, save it, close everything and open your game to find that your beloved buddy is back!

Do not forget to backup your data1.dat AND save files.

For those having problems with opening the data1.dat file, follow these steps.

• Download the MGSV QAR Tool[www.nexusmods.com].
  
• Create a folder in Steam\SteamApps\common\MGS_TPP\master called “QAR Tool”.
  
• Extract the contents of the archive you downloaded into the new folder.
  
• Open Run from the Start Menu.
  
• Type cmd and press Enter.
  
• Type cd C:\Program Files (x86)\Steam\SteamApps\common\MGS_TPP\master\QAR Tool and press Enter.
  
• Type MGSV_QAR_TOOL.exe “C:\Program Files (x86)\Steam\SteamApps\common\MGS_TPP\master\data1.dat” -r and press Enter.
  
• Once it’s unpacked, use Notepad to open data1\Assets\tpp\script\lib\TppStory.lua
  
  There you go, please leave any problems in the comments bellow.
  You can also search for the QAR Tool on NexusMods under MGSV Ground Zeroes mods.

While the original method works just fine, you can still have Quiet as your buddy forever by others means, them being:

• Not maximazing her buddy level, by any means necessary. Not maximizing her buddy level will not trigger the event where she runs off.
  Be aware that this will stop the main quest from progressing and you wont be able to get 100% completion.

Alternatively

• By putting the Butterfly(front) design on your emblem before you finish Mission 41, her quest wont progress and she'll be stuck as your buddy. You wont be able to get 100% completion.