Yes, we have tools to look closer at what is happening. We have a tool to save the memory contents of a windows process. So you can use this on the EVE online client to record its state.
There is a guide on how to use this tool at How to Collect Samples for 32-bit Memory Reading Development
When we have a process measurement, we can use the memory reading code on this as well to inspect where it goes wrong.
A process like the EVE Online client can ask windows how much memory is available or free. It can then adapt the way it stores things in memory to this limitation. So this could lead indirectly to the correlation you described (Dependency of the problem on the number of instances per machine).
An idea is to collect a sample of the EVE online process when you observe such a problem (using the guide from How to Collect Samples for 32-bit Memory Reading Development) and then take a closer look at the memory reading with this sample.