Note, it is not possible to save the game during combat, braindance and some quests.
If you encounter issues with saving the game in other circumstances, make sure that Cyberpunk 2077 folder is not controlled by your security software.
Windows Defender and Bitdefender are examples of security software that may be related to the issue:
If you are using Windows Defender:
1.Open Windows Defender Security Center.
2. Click on Virus & threat protection.
3. Click the Virus & threat protection settings option.
4. Under "Controlled folder access," click the Allow an app through Controlled folder access link.
5. Click the Add an allowed app button.
If you are using Bitdefender:
1. Go to the Dashboard of BitDefender
2. Protection tab on the left
3. Click on Application Access under the Safe Files applet
4. Flag the check mark for Cyberpunk 2077