For all the players who are loosing mission progress after multiplayer please see this thread and help us collect more detailed information.
Also please note:
To avoid some confusion about how the mission system is supposed to work in MP I will try to explain with some examples.
Adam has made progress and completed 3 missions.
Eve has made progress and completed 2 mission and she is currently playing mission 3.
Scenario 1 (When the guest can save progress):
- Adam joins Eve’s game (eve is hosting, Adam is guest).
- They play and finish mission 3 together. Adam has already finished the mission so it won’t impact his progression.
- When they start playing Mission 4, Adam will start making progress that should be saved for him when he returns to his game.
Scenario 2 (When the guest will not save progress):
- Eve joins Adams game (Adam is hosting, Eve is guest)
- Eve will see Adams missions in her log and NOTE the save icon being crossed over. This will notify her that they can play together, but the progress for mission 4 will not save for Eve. It will save for Adam.
- Once Eve returns to her own game, the missions she previously saw while in Adams game will no longer be in her log !
As a guest, if you check your log and you don’t see the save icon above under a specific mission, you will be able to play that mission together with the host and save your progression.
In both cases above, they will both save any loot picked up, any XP earned. Their achievements, collectibles, stats should also be saved for both.
Here is an update from the Dev Team
We are investigating, fixing and verifying many, many, many issues. Thank you to all of you who give us details around your issues and those who help others find temporary workarounds for problems.
Thank you!
Today we released the April update. Please see patch notes here: https://generationzero.com/en/blog/april-game-update-now-live
Versions:
XBox One: 1.0.5.90
PS4: 1.03
Steam: BuildID 3742329
We are looking into Windows 7 boot issue.
A workaround seems to be patient and then to hit esc a couple of times while on the black screen.
If you are playing on PS4 and have never registered to PlayStation Network (please note this is not the same as having PlayStation Plus) you will not be able to save.
Some users have reported that they can’t save while playing offline, these players all seem to sign in to their PS4 with users never registered to PlayStation Network.
Solution: Sign up to PlayStation Network (you will need to be online to do this step) and the next time you start the game you should be able to save. After that you can save during online or offline game play.
For May update please see our notes here:
Versions are:
PS4 1.06
XB1 1.0.6.26
For June update please see our notes here:
Versions are:
PS4 1.07
XB1 1.0.6.56
Steam BuildID 3933731
June hot fix is out. Fix for crash when using fireworks.
Versions are:
PS4 1.08
XB1 1.0.6.66
Steam BuildID 3969641
For our August update please read our patch notes here:
Versions are:
PS4: 1.09
XB1: 1.0.7.12
Steam BuildID: 4110341
For September update please read our patch notes here:
Versions are:
PS4: 1.10
XB1: 1.0.7.41
Steam BuildID: 4218799
For October update please read patch notes here:
Versions are :
PS4 : 1.11
XB1 : 1.0.7.62
Steam BuildID : 4309776
Hello!
For November update please read patch notes here:
Versions are :
PS4 : 1.13
XB1 : 1.0.8.10
Steam BuildID : 4411786
[PC Only]
We have a fix for the Alpine Unrest DLC “Not Alone” mission not unlocking for players who have completed all missions in base game.
Steam BuildID: 4438285
We will roll out the same fix for console as soon as possible early next week. In the meantime there is a workaround that has solved this issue for some people. Join another player who has the DLC but not yet started on the objectives of the mission. Once you have the “Not Alone” mission in your log, you can go back to your own game and it should have become permanently activated.
Thank you for your patience and all your kind words. 
Hello!
For January update please read here:
Versions are :
PS4 : 1.15
XB1 : 1.0.8.66
Steam BuildID : 4572857
Hello! 
For more detailed info on the February update please read here:
Versions:
PS4 : 1.16
XB1 : 1.0.8.96
STEAM BuildID : 4675726
For the March release please read the details here:
Versions:
PS4 : 1.17
XB1 : 1.0.9.33
STEAM BuildID : 4807514
Happy Anniversary! 
We have a fix for an issue where your crafting stats would not save after restart.
Versions:
PS4 : 1.18
XB1 : 1.0.9.38
STEAM BuildID : 4827006
April Update information is here:
Versions:
PS4 : 1.19
XB1 : 1.0.9.67
STEAM BuildID : 4935353
June Update information is here:
This is update is for Steam only at this point. Consoles will be updated as soon as we can. Due to the pandemic, some things take a little longer. Thank you for your patience.
Versions:
STEAM BuildID : 5179689