I just tested on your site (I found the same page above). In Chrome on a Mac, I was able to paste text indefinitely in that box. It made it down to the map and then stopped growing, though I could add more text.. but the buttons were shown. I'm not sure why you're seeing something different. There's nothing on the page that looks like it should overlap the message box and cut things off, so I'm just not sure what would be happening.
Can you test the Send button from a page on our blog to see if it works for you when you add a lot of text?
www.sourcecoast.com/blog/jlinked-v2-1-im...linkedin-integration
Knowing how that compares for you will help us understand what may be wrong.
Thanks,
Alex