Thanks for the report. This can happen on sites which perform an exceptionally high number of database queries, trigger a high number of PHP errors, or otherwise use a large percentage of the available memory limit on your server. Sometimes the amount of data that has to QM collect will cause it to go over the memory limit or cause other problems.
In this case, the request to the server often succeeds but the response won’t make it back to your browser, either due to memory exhaustion or, if you’re using an Nginx proxy, response size limits.
I don’t have much advice other than to try addressing any PHP errors that Query Monitor reports (or that you see in your PHP error log) and to try switching your theme to one of the default “Twenty” themes to see if that helps. Basically, try to reduce the amount of data that QM has to collect and display back to you.
I understand this is ironic given that QM is intended to help in this situation, but there’s nothing it can do about memory limits or server resource restrictions.