OK, so the triggers look identical... you are sure that is the local checkout and summary triggers?
These triggers are "current page submit" triggers... they include intrinsic validation of sorts that makes sure someone has submitted the current page. However, it uses the HTTP_REFERRER value in order to do that, and sometimes, some people, will have that value blocked and removed from the header by antivirus or security software.
This trigger may not work for some people for that reason, so if you were using a different trigger for the local checkout that succeeded, I would have thought that was the culprit.
If they all use the same trigger, then the only way for some of the transaction to take place and then not the rest would be if it thought the transaction had failed, but there is no difference in the Response Code values, so that doesn't seem to be the case.
Unfortunately until we can reproduce the problem it will be difficult to diagnose. Double check to make sure the triggers are the same, but it appears they are.
