The only way that the L5 will suddenly shutdown it is if the L5 get really hot, or break a critical dependencies, there is a troubles when the machine suddenly shutdown, something will never boot because a broke filesystem, this behavior has happened to me on gnu+linux OSes.
There is a tools called Jumpdrive to recovery the L5 sadly I don’t know how it works but there are other people here more expert than me about Jumpdrive like @Quarnero
To Reburn PureOS you can follow the instructions: https://puri.sm/posts/reflashing-the-librem-5/ this post it out to date, so replace that step for: Librem5 / librem5-flash-image · GitLab and last step librem5-flash-image --dist byzantium --variant luks exemps: New Post: Reflashing the Librem 5 - #33 by carlosgonz
Please before Reburn PureOS take the time to learn good all the documentation for reburning… if it is the first time doing this do not be hurry and wait to learn good all the documentation, Librem 5 it is NOT a conventional phone like others, it very very import to learn all the documentation only doing this will safe prevent that you broke your L5 again.
After Reburning PureOS make sure that all Firmware and Driver it up to date specially the bootloader das-uboot.
Additionally you can try Rescue before Reburn like remove the battery and let get the L5 get cooler later put the L5 on Lockdown mode(ALL HKS OFF) insert the battery turn ON by pressing the power button 5 sec, if not boot with 5 sec pressing, try with 20 sec power button long pressing.