Memory pressure can trigger paging and garbage collection. Both introduce latency which would not be present otherwise.
GC'ing 32GB of data can take seconds. Why would all app processes GC at the same time? Because at about 95% memory utilization Windows sets a "low memory" event that the CLR listens to. It will try to release memory to help other processes.
If the applications get into a paging frenzy that would also explain huge delays in normal execution.
This is just guessing, though. You can try proving it by looking at the "Hard page faults/sec" counter. There also must be a counter for "full GC" or "Gen 2 GC".
The fix would be running at a higher margin to the physical memory limit.