Seems odd that it's intermittent, especially given the static IP, i could understand if it was DHCP as it may be related to lease length.
When performing a constant ping do you also drop packets which correlate with the timeout of the GUI?
Hi
Is there a DHCP with an overlapping range?
can you see the connection from any of the network switches ?
Thread reported, hopefully a moderator should now move it to the area for ESXi.
The intermittent nature of this really sounds like you have a duplicate IP conflct going on. I'd make sure the host address is excluded from any DHCP pools and you don't have another device sitting on that same address.