Thank you, QuilterC, for your suggested workaround.
I have been having this problem for about a fortnight.
For Microsoft's attention (I could start another question as this is important enough, though it seems to make sense to report here at the moment),
this is a fundamental issue for me. I use OneNote for every day across four devices, each with different versions of the software as follows:
OneNote 2010 (Windows 7 desktop)
OneNote 2016, installed through an update request [OneNote 2010 is also installed, though I have not opened the 2010 version since starting to use OneNote 2016, which might have been from first use.] (Windows 10 laptop)
OneNote for iPad - latest version
OneNote for Android on Samsung phone - latest version
My notes have been dropping out of my Desktop for the past fortnight or so. I read a forum entry which said that having a caret symbol (^) in a notebook URL started causing an issue at the end of 2016, so I closed those of my notebooks which had a caret
in the URL. I re-opened them using the 'Open in Desktop' button in the OneNote Online version. Even so, I am still losing access to my notebooks several times a day.
I find that my notes are available on my other devices, and up until now, I have been using those as a workaround until the information reappears in OneNote 2010 on my desktop.
Local backups: in both the OneNote 2010 and OneNote 2016 versions I am using, I have increased the frequency of the local backups to daily and the number to 3. I want to retain as much of the notebook information in multiple locations as possible in case
I ever lose access online.
I am wary of upgrading the version of OneNote 2010 on my desktop, where I have Office Professional 2010 loaded, in particular because this machine is still on Windows 7.
I would be grateful for Microsoft to review these OneNote 2010 issues and fix them permanently.