Hello, I hope everyone gets a copy of this message. The issues that are/were being noticed in the initial page of the Sucuri plugin (aka. the dashboard) may be caused by two different things: the latency in the connection between the website and the Sucuri API service, and the slowness of the file scanner for the core integrity checks.
For the first thing, the latency in the HTTP requests against the Sucuri API servcie; this is a temporary issue, normally it should not take more than one second to retrieve the information from the API to populate the audit logs panel, but in rare cases it may happen that the connection is reset or the some unknown and temporary issue the request takes more time to finish.
As for the second reason, the slowness in the file scanner; this is a tricky one because the performance of the code that I implemented to scan the WordPress core directories relies on built-in functions provided by the PHP programming language, so the performance depends on the version and configuration used to compile that program in the server of each website that is experiencing the issue, I have no control over this; during development I test the code against different versions of PHP (5.3, 5.4, 5.5, 5.6, and 7.0R5) and have not had any issue with any of them, so the issues that you are experiencing are from a special configuration of your server which is affecting the performance of the code making the scan of the file system slow.
Note that the core integrity checks can be disabled from the scanner settings panel located in the general settings page of the plugin, this information is more or less the same as the one provided by the audit logs so you can safely deactivate that and keep using the other panel.
As for the slowness on the last logins page, this is something similar; the information of the failed logins is stored in a plain text file in the uploads folder, depending on the number of attempts executed against your website the file may increase in size (very common in brute-force attacks); PHP is not allowed to allocate unlimited data in memory so after certain limit (configured by your hosting provider) it stops and the process is killed following a blank page as you people have already seen; the solution is to reset the content of that file so the PHP interpreter can read it with less data, you can do this clicking a button located in the scanner settings panel located in the general settings page.
I hope this explains the issues and that my suggestions work for you, I will mark this ticket as resolved but feel free to reopen if you need more information; if you want to ask more questions please open a new ticket.
