There is a patch( ESX350-200712401-BG) available for update of bnx2 driver to address the following issues:
An issue with the BCM5709 firmware where ping requests sometimes fail after loading and unloading the bnx2 driver.
An issue with the bnx2 driver where a device using the bnx2 driver fails to connect to the a 100 Mbps network during the network autonegotiation period after system boot.
Link for ESX 3.5 patches:
Link for the related kb:
Note: Patch bundle ESX350-200712407-BG must be installed prior to installing this patch. The esxupdate utility will check to ensure that ESX350-200712407-BG is installed before proceeding with installation of this patch.
See if this solves your problem.
If you found this or any other post helpful please consider the use of the Helpful/Correct buttons to award points