Perhaps, in this situation ESXi host would have stopped logging. Once the scratch partition destination drive goes offline or inaccessible, syslog deamon will stop functioning which will ultimately stops logging. There wont be any PSOD due to that
You may try this on one of the ESXi host and check if it works for you
1. Login to ESXi using ssh
2. check if host is logging properly
3. Change the scratch partition to different directory
4. run this command
ps |grep -i syslog
you will get output with ps names vmsyslogd
kill the parent process using kill command
kill -9 <pid>
5. rerun command ps |grep -i syslog , check if you got new pid
6. Check if logging starts again and new logs created at the new directory which you specified.
Do the above task on one host and check if it works before proceeding with other nodes.