For us, this issue seems to only occur when we have many layers in the map (we have 43 in the project with the issue). It appears that the more layers turned on, the worse it gets. We have also noticed that this only occurs in the data view. The measurement tool seems to work fine in the layout view. The solution, if this is what's happening to other people, could be to create a Reader project that excludes the data view, unless there's a specific reason for including it. If that's the case, then you may have to modify your end-user workflow plan to ensure measuring occurs within the layout view. I suspect that in our case, the end-users are going to have to modify their workflows as most are not very confident in their GIS abilities; they know what they know, and to add another tool or two to achieve the same result by eliminating a view, would turn their world into chaos.
Hope this is helpful to someone.
Bryan