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Basically, your web map is too big for IE to handle. Your web map is 8MB in size. Shapefiles, CSVs and GPX files added to the map are all drawn by the browser. You are running into limitations of the IE browser's ability to draw features. IE 7 and 8 are not able to handle the number of features in this map. The only solution is to generalize the data even more than ArcGIS Online can do. If you have ArcGIS Desktop, you can generalize your data more so that it can be viewed. Another solution is to host the data on ArcGIS Server.
Here's a help topic that addresses this as well.
The important section on web map size is this:
Large amounts of data in a layer or the map may affect the performance of the map. For example, you may lose the map you are working on if you navigate away from the map viewer when the web map is too big for your browser to cache (generally, bigger than 2.5 MB, except with IE7 [64 KB] and IE8 [530 KB]). To help prevent this, sign in before you start working and periodically save your map, especially if you add a large amount of data.