thanks for your post, and sorry for the trouble.
This could indicate the server does not like something in the request. It might indeed be possible that the size of the table results in a lot of memory being used. Some servers then stop the execution and simply return a "404 Not Found" error -- although the file clearly exists.
Unfortunately, this is nothing that I can influence in TablePress, as it affects the server configuration. I can therefore only suggest that you ask your webhost company about this. They should know the reasons for why the server returns that "Not found" error.