Note: This issue is System 6 specific.
Most often, applications unexpectedly quit because they ask for more memory than has been allocated to them, the Memory Manager says "no", and the application has no idea what to do next.
PrintMonitor, even though it looks like a standalone application, does not use the RAM allocated to it during the background printing process. Instead, PrintMonitor uses some of the RAM allocated to the Finder. If the Finder (in the background) is maintaining a lot of items, such as open windows, mounted file server volumes, and so on, there may not be enough RAM left over for PrintMonitor to work. Try allocating more memory to Finder, such as 320K (the default is 160K).
Another possible problem is a corrupted Backgrounder file, the INIT that handles the background task management. Since PrintMonitor is appearing periodically to check the Spool Folder, it's probable that Backgrounder is fine and you're seeing only a memory limitation.
And finally, there may be an INIT that is conflicting with PrintMonitor's operation. Removing all non-essential INITs and testing will tell you if that's the problem.