Replace the HDD then.
My guess is that is completely unrelated to performance or anything. It's probably some shutdown/startup/login script or performed done during those, making it an issue of the GuestOS. Maybe something trivial such as unresolvable names/faulty nameserver (responses), firewall-blocked connection timeouts or something similar.
If normal operations of the running system are fine, there is no ESX(i)-side reason why it should be "slow" during those specific times only. Check the disk latency/throughput/IOPS when experiencing it.