Unfortunately, it looks like 4.1/Jelly Bean is more restrictive about accessing logs, so we might need to find another method to see what's happening.
Update: it looks like you can generate a bug report in JB (on some devices) by pressing and holding the Volume Up and Down buttons together for at least 10 seconds. Let go and it should ask where you want to save the files that are created (email, Dropbox, etc.). Please try again to open the Eye-Fi app, and if it crashes, follow those steps to create a bug report and send that text file to us. You can post it here, or email it to email@example.com
in case you don't want it to be public.