I installed a fresh Vmware ESXi Hypervisor on a fresh Dell PowerEdge T110 ii at 220.127.116.11 (static ip)
Occasionally, VMware disconnects and I can't reach it neither by web (https://192.168.0.10/) nor on SSH. But I can successfully ping the instance all the time, so I assume that it is not a network problem.
Whenever I connect a keyboard to server and press a few keys, the connection comes back.
You might have an IP conflict if you can always ping but actual connections reset randomly.
If the pings were occasionally failing I'd say that when I see this behavior it's because one of the vmnics assigned to the vSwitch is not on the same network (or the VLAN tagging is off on the switch or some other reason) and the round robin or IP hash algorithm is occasionally firing packets down that bad link.