I tried to repeat your problem and that did not happen. I created a table and below the table added some words. I set entire document to read only and then select a few cells in table and set it so that everyone can edit those cells. I protected the document with now password and saved it. I then closed it and opened it. I typed in a word in one of the cells then hit space bar and I just got a space.

What happens if you create a new document and do what I did above? See if you can recreate this in a new document. There may just be something wrong with that document.