Hi Benjamin. To recreate this problem, try move around with the sections under the option page. After I got it to work on my girlfriends website, see wanted to alter the sections setup. After reordering the setup she pushed the Save button and suddenly it all was gone, and the resume page made the error, telling that the data was to big to load into the page. So I think the reordering is giving some problem with the database. My suggestion is, if possible, make a new database for your plugin and let all data store inside of that one. But its just a suggestion, my database knowledge is not good.
I had exactly the same thing happen on my site. I updated my resume, changed the order and got the memory error that nothing could fix.