I have asked this question on several email lists and cannot get anyone to try my exact steps. So, I will simplify and ask here.
Minimum number of steps to recreate the issue:
1. Open a blank session of ArcMap (not an existing MXD). I am using ArcMap 10.6.
2. Add the ESRI World Imagery basemap.
3. Using the Go To XY tool on the Tools toolbar, navigate to X: -13,842,726 Y: 5,366,058, drop a point, and zoom to a scale of 1:10,000 (this should navigate you to the south spit of the mouth of Coos Bay, Oregon).
4. Using the Data Frame Tools toolbar or Data Frame Properties, rotate the data frame to 322 (this should give you an image that looks similar to the attachment). Note the hi-res vs. lo-res imagery within the data frame.
5. Change your zoom scale to 1:5000.
6. Perform a Redraw, using the Redraw button at the lower left corner of the Data Frame.
At this point, you should be experiencing the error. The globe in the lower right never stops spinning and the point that was dropped at the X,Y coordinates never shows up. It appears to be in an endless loop of trying to draw imagery.
This seems to be a problem only where hi-res upland imagery meets lo-res ocean imagery, and so far is limited to ESRI World Imagery (NAIP works fine). Panning inland clears the problem, but I am doing coastal mapping, so it is not an option.
This issue will effect anyone who is trying to do coastal strip mapping, which commonly uses rotated frames (Creating strip map index features—Help | ArcGIS Desktop ) or rotated estuary mapping.
My only solution so far is to use NAIP instead of ESRI World Imagery. This is workable, but there are times when the ESRI World Imagery looks better than NAIP.
I guess the question is: Can ESRI confirm this is a bug in the curated ESRI World Imagery?