Update: The issue has been fixed.
Konami has issued a (temporary) solution for a certain glitch some players are experiencing in MGSV: The Phantom Pain. This glitch prevents the player from progressing past Mission 42 or 29. It happens when Quiet has been selected as a buddy, so the temporary solution is to simply not use her for Mission 29 or 42, for the time being.
The official announcement is as follows:
Update: More information regarding the glitch has been added.
In addition, the official Metal Gear Twitter posted the following:
An issue has been reported where the game will persist in a continuous loop on a black screen; the team is looking into cause & resolution. Until updated; please avoid playing missions 29 & 42 while using Quiet as your buddy, as this seems tied to the cause of the issue.
So until an official resolution has been made available, you have been warned!
Source: MGSV Official Site, Metal Gear Twitter