Hi,
thanks for your question, and sorry for the trouble.
That white screen most likely is the result of the memory limit being reached, so it’s not really possible to determine the “offender”.
So, instead, you should set the WP_DEBUG constant to true in your wp-config.php file. After that, you should see error messages instead of that white screen. If those refer to the memory limit being reached, I suggest to increase the current limit by following the instructions at http://codex.wordpress.org/Editing_wp-config.php#Increasing_memory_allocated_to_PHP
Now, regarding your tables: Sure, you can save those. The best way should be to export them to the CSV and JSON formats (on the “Export” screen of TablePress). With the CSV format, you’ll have files that can be opened locally as well (e.g. in Excel), while the JSON format is the best for restoring the tables in TablePress (if that ever becomes necessary).
Regards,
Tobias