You can probably set the service to restart if it quits - in the Recovery tab of ths IIS service (World Wide Web Publishing Service), when running services.msc - but it's likely a symptom of another issue, as you suspect.
I have had services quit without warning, when a hard drive of a mirrored pair was failing, for example. Obviously there can be other reasons. You might try a chkdsk x: /f (where x = the drive letter) from an elevated command prompt, which would require a server restart if it's the boot volume. If it's not the boot volume, you might want to stop the SM service and IIS before commencing.
As Bruce is suggesting, check the logs (including Windows events).