Try this instead. Click the "reply" button on the bottom of the post you're looking to quote. That's instantly put the post in the "Write your reply" box. If you're doing several on different pages, after each one, click the file box with the green dot in the top right corner. It'll say both "Save Draft" and "Delete Draft". Click "Save Draft" then go find what you want to quote next. That'll save your work.
Before finding your next quote, be sure your typing line is on the white, not in your previous quote. If it's in the previous quote, your next quote will go inside it.