I've continually ran into this error. I will connect to several shape files and often one of them will not draw on the map. The data can be viewed in the data table but it is all grayed out. When a specific feature in the data table is selected, it is highlighted on the map, but as soon as it is de-selected, it disappears. My co-worker next to me has connected to the data and is viewing it fine. This happens when neither of us are editing. Today I tried using an older version of the same shape file that didn't draw, and it worked fine. However, one of the layers that previously was working properly disappeared and the data table was grayed out just like the other! I am using Map 3D 2014.
That seems to have worked. I am actually using Arcmap while my coworker is using Map 3D. As long as she opens her file first, all appears to be ok. We are not editing the same shape files at the same time, but we are viewing them at the same time.