thanks for the link.
I can confirm that loading is very slow, and sometimes stops with that error message.
I'm sorry to say it, but this is a case where the used way of showing the table is just not optimal. A table like this with over 4,000 rows and 15 columns means over 60,000 cells to handle. This can unfortunately get very slow, and in your case also results in a total file size (of the page with the table) of over 2.5 MB. This is a lot of data to transfer, especially on slow internet connections.
As I can imagine that you're planning to use more large results tables like this on the website, I strongly recommend that you switch these large tables to a custom PHP/mySQL solution, and only use TablePress for smaller tables.
In the long run, this is the best solution, as you'd just suffer from a slow site if you create more tables like this in TablePress. I'm afraid that such large amounts of data are just too much for TablePress to handle directly.