I can imagine your frustration with not being able to use your data internationally. I know that if I am in a place that is unfamiliar to me, I do like to do research on my phone. I have consulted with Apple directly to find out what could be causing this issue. The have provided me the following steps, if you are still experiencing the issues after these steps; our next move would be a different sim card. Please use the links for the steps. http://support.apple.com/kb/ts3780 and also http://support.apple.com/kb/ht1807 I hope this helps out.
My boyfriend and I both have iPhone 5's under the same Verizon account. He travels overseas 3 out of 5 weeks. He has the opposite problem as the author of AJSPaint. He is able to use wifi the vast majority of the time. Every now and then he has to turn on cellular data when there is no wifi, but only for a few seconds. In those few seconds, a flood of messages and emails come in, many that were sent hours or even days ago when he had a wifi connection! Why didn't they come through then? It's like they were hovering in cyberspace just waiting for the cellular data to be turned on. The Global Data Roaming charges mount up instantly. Any suggestions on how to improve the wifi connection so the data comes through when it is supposed to?