Merging of ETL files has failed (0x80070070) (Flags: 0x0000011f)
Previous search gives little answers as to why, but the problem seems related to Windows' event logging service. Comments on this similar question suggest it's related to disk occupation, but with no source. My SSD is indeed almost full, but with 6 GB of free space.
I resolved the issue, the multiple times it happened, by restarting windows and then start the profiling as first thing as the OS is ready. On a fresh start it works, but going further with changes and profiling it eventually appears again.
If someone knows a long-term solution feel free to add.