There's not a common problem with Safari, but there can be issues others are experiencing with Safari that may seem similar. We've worked to fix those over time, and what you're reporting is not something we've heard of before.
When I tested on your site, here's what I did. It's a little different than what you tried, and may have somehow changed the behavior:
1) I went to your App Canvas Page
2) I then when to you're actual home page, outside of the Canvas view
3) On you're 'live' site, I found the page where you have the "Facebook" login button
4) I looked at the code on that page, and tested to make sure the login with Facebook functionality worked in that view... it did, as expected
5) Then, I went back to your Canvas page and tried to login there. It worked there as well.
There shouldn't be any reason that logging into your 'live' (non-Canvas) site should make the Canvas work, but that's what I did.. can you try testing that way to see if that changes the behavior you see? If so, we'll gladly investigate further, but I'm simply unsure what is different about your site vs others.
Thanks,
Alex