MacBook Pro goes into deep sleep when battery is half full

You can try running the Apple Diagnostics to see if any hardware issues are detected. Chances are the battery has a hardware issue that only occurs at a certain charge level which can be hard to detect so the diagnostic may not detect the failure (try to run the diagnostic while the battery charge level is in that potential bad zone. Most likely you will need to have the Battery replaced.

If you have the non-Touchbar model, then see if your laptop may qualify for this free Apple Battery repair program:

https://support.apple.com/13inch-macbookpro-battery-replacement

https://support.apple.com/13-inch-macbook-pro-solid-state-drive-service

FYI, here is the current list of the publicly acknowledged free repair programs for various Apple products (some products may have multiple programs):

https://support.apple.com/service-programs

Like I said most likely your battery will need to be replaced. The only way I've been able to locate some of these odd battery failures such as you have described is by running a system stress test which can sometimes trigger a battery failure since a stress tests causes the battery to drain as fast as possible. When the charge level hits the level which has the problem you may see the laptop shut off or you may see the charge level drop more significantly if you are monitoring the charge levels during the stress test.

I use the "mprime" app in Torture Test Mode and I use an Apple command line utility in the Terminal app to log the battery charge levels so I can review them later. The following command will log the battery & charging/discharging information to a "battery-log.txt" stored on the Desktop:

pmset  -g  rawlog  |  tee -a  ~/Desktop/battery-log.txt

You need to press the "Return" key at the end of the line to execute the command. To stop logging the battery information you will need to type Control + C in the Terminal app. Each time this command runs it will append to this file if it already exists.

Even this may not be enough to identify the problem or even reproduce it.