I don’t believe WordPress itself has a max size. However, the database behind it has a max length that the wp_posts.post_content field can be.
If we look in wp-admin/includes/schema.php, we can see the SQL used to create the wp_posts table:
CREATE TABLE $wpdb->posts (
ID bigint(20) unsigned NOT NULL auto_increment,
post_author bigint(20) unsigned NOT NULL default '0',
post_date datetime NOT NULL default '0000-00-00 00:00:00',
post_date_gmt datetime NOT NULL default '0000-00-00 00:00:00',
post_content longtext NOT NULL,
post_content is a LONGTEXT type of field. That may mean slightly different things depending on your database.
Looking up the MySQL length for LONGTEXT, you’re looking at 4294967295 bytes or roughly 4.2 gigabytes. You’re probably no where near close to that, however, you’re probably at the point where either your database, web server, or some other part of your pipeline is giving up because there’s too much to handle.
Also note that the data is form submitted and POSTed back to the server – according to this answer, there are several factors that come into play when it comes to POST data length limits.
To summarize: it’s hard to tell what exactly is causing your problem, and without some trial and error on your part, and your own investigation, you won’t find much of a solution here that deals with your immediate issue.
However, I would propose that you work to find a better solution that storing this in the post content. Honestly, even storing each new entry in it’s own post_meta field would be better to some degree. Ultimately, moving this much data around in a single page is going to be problematic – it’s already an issue for you, and it will only get worse.