Actually the issue isn't with Direct Mode, it can happen over wi-fi also. Unfortunately iOS is rejecting the videos shot by your camera and won't let us save them.
Apple tends to be particular about which combination of codecs, format, and dimensions it will allow third-party (non-Apple) apps like ours to save. The Eye-Fi card and software have no problem with the videos, we will upload any photo or video with an Eye-Fi compatible filename.
Please visit this thread viewtopic.php?f=17&t=6129
for some discussion about it.
Try shooting lower resolution to see if iOS will accept the file. If you're shooting .MTS, iOS doesn't currently support that at all (as far as we know) so please switch to another format if your camera supports it.
Sorry there's no fix for this but I hope the information is useful.