When user, in Microsoft Excel 2016, presses the "check out" button, a loading "Check out file..." window opens and never finishes loading. User has the proper permissions and I don't see any obvious reasons why it's not letting her checkout. Any thoughts or guidance would be appreciated!
Might be issue with the Services not running properly or some jobs not responding correctly. Do an IIS reset and then check if you are still facing this issue. Idealy you should not, but if the issue persists, try once from SharePoint Designer.
I had a similar issue recently. SharePoint free disk space requirement (installation drive partition) is 5x memory, in my case that is 40GB. The site locked when the available free space fell to approx. 40GB while I was in the act of adding more disk space. Later, I noticed when attempting to Check Out a document, I was prompted to supply credentials and the dialog boxes above appeared. Some items were also grayed out on the site Ribbon. To resolve, I simply opened Central Administration > Application Management > Configure quotas and locks, then chose the desired Site Collection / Web Application and selected the "Not locked" option.
I hope this helps someone else!