We are getting these error dumps as posted above also and "Failed to obtain item from data store for given id: ()" also. The admins set us up to do everything as shared to start and not use dedicated. As we migrate to the new server more and more we started getting these errors and really poor performance on some bigger layers like polygons and image services. Some will not draw at all and just site there. Often we get totally white maps.
We doubled the number of shared instances but still having issues. Seems like moving anything that has issues to dedicated has helped. But some still did crash out saying out of resources when set to 1 and 2 (I am thinking 0 min 2 max is best?). We have over 300 services now (but 50 some are just views) and have it set to 16 instances (was set on a 8 core with 50 for each (which I think is the default). Server CPU under 30% and RAM under 40% used. Its a Azure VM.
They come every second or so. Often we can hit one and its fine but hit a second and it starts in the log. We do not have too many users on yet so not sure what will happen then. Polygons in a Ops Dashboard make it the most mad.

I am thinking we wack-a-mole any service that is slow and change to dedicated? Or you seem to say just put the little ones that are not used much to shared then ones we know are big or used a lot to dedicated? And set to?
Not finding too much on this so any help is greatly appreciated! Been on it a week already.
thanks for any info @JakeSkinner I think we may have met in the past.