Hello KR00,
Welcome to Microsoft Community.
I very much understand your need to carry a laptop with you and if the cover is set to "Do nothing" it is a very battery draining setting that will drastically drain the power reserve in the battery.
I know this makes you feel uncomfortable, but just as a personal recommendation, I highly recommend carrying a power adapter in your laptop bag to avoid losing important data or running out of power in the middle of your work.
In response to your question, I may need to explain to you the standby state of the laptop and the difference between sleep and hibernation, if you are patient and willing to learn about this, you can carefully read the information in the following links:
Shut down, sleep, or hibernate your PC - Microsoft Support
System power states - Win32 apps | Microsoft Learn
The link describes the standby state S0-S5, corresponding to the working state, sleeping state, and hibernation state respectively.
Therefore, you first need to confirm that you have properly set up the closed sleep action by following the linked instructions.
Second, check if the standby state of your computer has been changed.
Finally, check to see if your laptop automatically shuts down due to low battery.
Also, as an added tip, if you are used to Office software, get in the habit of Ctrl+S whenever you edit or change a document, which is the shortcut key for quick save. For the browser, please set the browser to automatically open the page that was not closed last time when you open the browser again. This can effectively prevent misoperation from closing the page that was opened.
Best regards,
Mitchell - | Microsoft community support expert from MSFT