Hi,
I am using WordPress 5.6.2 and WP Mendeley without any problem. A couple of days ago I used customised CSL and experimented with different interesting ways to display the references + abstracts without experiencing problems (If I am allowed, I will post a link here when I finish writing the post ?? … shameless self-advertising ?? ).
From my experience usually the problem is at the mendeley end. Did you try refreshing the token? Try to clear the cache and refresh the page.
A good way to check whether the token is still valid is to request the collection IDs in the settings. If that does not work, it’s very likely that there is a problem with the token.
For my website I have the “Never refresh” option selected because in this way I choose when the list needs to be updated. It also prevents cases where suddenly the page is empty, like in your case, but without a clear reason.
I hope it helps. If it does not, the next step is to enable debugging in WordPress and see whether the errors you see are meaningful.
Constantin