Hi Jesseb,
Could you tell me which version of office and Windows system are you using?
Based on your description, you want to know the reason of OneNote print driver keeps missing.
Your issue might be caused by several reasons. Maybe something on your computer is messing with installed printers. We dont know what it is, you may try running under a less privileged user account to see if any program attempts to remove printers.
Or you could check if your computer install any third-part programs or any updates recently. Maybe this is one of the reason for you issue. And perform a clean boot in Windows is a good choose, this helps eliminate software conflicts that occur when you
install a program or an update.
More information about performing a clean boot please read this article.
https://support.microsoft.com/en-us/kb/929135
And you can also refer to this case to try these methods:
https://social.technet.microsoft.com/Forums/office/en-US/45f4d2ff-ee8b-4213-9138-3ad635bb940e/send-to-onenote-2010-printer-missing?forum=officesetupdeployprevious
There is an article about XPS printer with OneNote Printer, this maybe not the reason but you can read this article to get more information:
http://blogs.msdn.com/b/johnguin/archive/2010/10/07/the-xps-printer-is-needed-by-the-send-to-onenote-printer.aspx
Hope its helpful.
Regards,
George Zhao
TechNet Community Support