Wordfence scan stops responding or is stuck

I have WordFence on two of my websites. One is strictly WordPress (installed in /public_html.) The other site has WordPress installed in the /public_html/blog folder.

On the first site (www.uniquebeadedearrings.com), WordFence stopped completing its scans. it would “stick” at this point: ‘Fetching core, theme and plugin file signatures from WrodFence’. I switched off a few options, restarted the scan and have had zero problems since.

On the second site – https://www.webthemedesigner.com/blog – (which is on the same server!) the scan “sticks” at the same place and has never completed even once. I’ve done the same as above as well as everything that was suggested on the support page – to no avail.

I’m on a shared host, so I cannot change parameters of the server such as max_execution_time or memory_limit.

Any suggestions are welcome.