How is the JFBCInvite module currently configured? The columns and rows settings are only available if you're using the "Full" view. The condensed view is much more strict as to what you can do with it, and that's mainly dictated by Facebook.. leaving us with little/no options.
The automatic resizing is our method to fix the preview box from being cut off when using condensed mode. However, it uses javascript and has some limitations. Please make sure there are no javascript errors on the page with the invitation module. It's best to test this with something like the rhuk_solarflare template by doing the following, as many templates are javascript heavy, and buggy:
www.yoursite.com/page?template=rhuk_solarflare
See if that helps, and look for errors (these are displayed differently in each browser) and let us know what you find out.