I updated your wp-config.php file to increase the interval between autosaves, and at the same time also increased the share of server memory available when in the back end (which is more resource intensive).
It still takes quite some time to load the page containing the View to edit it, but the back end is generally slow to open any pages, it's not specific to those with Toolset content.
But waiting, the editor does become usable.
We do have a project to rewrite the View block to make it less resource-intensive, but it ran into some problems with unintended side effects, and so I can't say how long it will be before we can look forward to those improvements.
I appreciate how frustrating it is working on your site, and I'm sorry for that.
When trying to update the homepage, the page is not saved and the error "Something went wrong while fetching the dynamic content from the selected source, with message: "You are probably offline" keeps popping up.
Nothing is solved.
The issue still appears on both the homepage, search propties page, Toolset template and who knows what other pages.
I visited the site and managed to load the page, although it did take a long time, and eventually it was possible to save changes to the page, it was a question of waiting, roughly a minute.
That's not a very good experience, but it should be possible to make edits to the View and save them.
I noticed while editing the page that it had a large number of revisions, which I deleted, and added a constant to your wp-config.php to resrict the number of post revisions that are saved.
I'm checking with my colleagues if there is anything else we can do to help.