You're definitely correct that it's a memory issue. However, it's not necessarily caused directly by JFBConnect. Each extension on your site uses a little bit of memory. Enabling any other ones, when you're already close to your memory limit, could cause you to go overboard. A 25MB limit is pretty small of a limit, but still is well within a normal amount that should be needed to load a page.
JFBConnect connect has been very optimized to be as fast as possible, while using as little memory as we can. On this site, for instance, most page loads are about 11MB, with some 'heavy' ones going up to 18MB.
I'd recommend seeing if you can disable other, unused extensions, or increasing your memory limit for PHP. Another thing to check is disabling our plugin and turning on the "Debug System" option within the Global Configuration area of Joomla. Reload the offending page, and you'll be able to see the memory used 'before' our plugin. If it's anywhere near 25 (or even 20MB), that would explain why enabling just one more plugin causes the issue. If it's under 15MB, then that could indicate an issue with JFBConnect, as we shouldn't use 10+MB.
Hope that helps you narrow things down,
Alex