Acrobat Distiller runs as an application program. There is nothing that it does or can do to literally “shutdown” your computer or for that matter to cause it to reboot.
My best guess is that there is some Windows driver problem or even a hardware problem that is triggered by the system resources used by Distiller. This could include RAM failures or disk drive failures. My recommendation is to run full system diagnostics on your computer and to make sure the operating system (I assume Windows here) is fully updated.
In future postings, it would be most helpful if you provided information as to exactly what operating system version and Acrobat version you are running.