Try the latest supported igb driver version 5.3.1 from here: (Make sure you reboot after updating the driver!)
https://my.vmware.com/group/vmware/details?downloadGroup=DT-ESXI55-INTEL-IGB-531&productId=353
VMware Compatibility Guide: I/O Device Search
If that doesn't help, please post the output of the following commands:
# vmware -vl
# esxcli software vib list | grep igb
# esxcli hardware pci list | grep "Device Class: 0x0200" -A20 -B15
Also check /var/log/vmkernel.log for any issues.
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