GGS SyntaX on TA wrote a good guide for this here
TrueAchievements and I will post the spoilers, as I feel they are very important, here:
*** Spoiler - click to reveal ***After starting the final process, you will loose Quiet forever!
If you want to delay this, simple use the “Butterfly” design for your emblem. You earn this for complete a mission with Quiet, where she does the most work.
To stop the delay, remove the emblem.
Just to note, I did copy paste the spoiler from his/her guide so ensure they are given credit for that. If you have not unlocked Quiet or are curious how to, here is a vdieo as opposed to GGS SyntaX's text guide: (credit to PowerPyx)
However, for those who are more inclined to a video walkthrough as opposed to a text guide here ya go:
(credit to HarryNinetyFour)
If you have any suggestions please let me know. Past that, good luck!