Libby books not syncing to Clara BW

I've borrowed several books through Libby, and despite trying to even manually sync my Clara, they will not show up on my shelf. I did a little digging and saw that Kobo isn't able to have books from Overdrive that they don't sell through their own store, but that doesn't seem to be the problem here. I went to check, and all of the books I'm having trouble with are available through Kobo. However, when I look them up on the Kobo store through my device, there's no option to borrow directly from the Clara, unlike several of the other books I've read. Does anyone know what might be causing this, and/or what might fix it?