We are very sorry this happened!
Unfortunately this means somehow your computer didn't write out the save file correctly and there isn't any way to repair these files. However, you should be to roll back to an earlier auto-save so there hopefully won't be too much progress lost.
Open your save file directory (change <user> to your own computer user name):
Here you will see file called "#.sav", where # is 1, 2, 3 or 4 depending on which save slot you were using. In addition, there are other files called "#_Day_##.sav". Those are auto-saves created at the start of each day.
Copy #.sav and rename it to #.bak and then delete the original file. Then, copy the most recent "#_Day_##.sav" that matches the slot you were using. Rename that copied file to be "#.sav".
Based on the following screenshot, we would rename "1.sav" to be "1.bak", delete "1.sav" and then copy "1_Day_77.sav" and rename it to be "1.sav".
Now when you load Firewatch and select Continue or Load Game, you'll be able to load into the beginning of the latest day you played and can continue playing from there.
If this does not resolve the issue for you, don't worry! Please contact us at email@example.com and we'll help you out.