Hello -
I'm new to ESXi, but will try to be as thorough as possible. My format will be to show the environment, cite the problem, then below cite the troubleshooting steps already performed to help you help me! 
So, I have 1 ESXi host, (HP DL380 G6)... It is running 13 VM's on it, newly implmented. The subnet it belongs to has ~50 addresses, with another 18 physical desktops in that subnet. The VM's are running XP SP3 32bit, 60gb, VMCI, and each has VMXNET3 adapter installed. The host has 4 NIC's..all hooked up with 1000/Full hard coded. Default settings largely, vmnic0/1/2/3 are all on vswitch0. They do plug into Cisco gear, but port security has been configured to a high limit (30), and no errors are showing on any of those 4 ports. (2 on 2 separate switches)
So I have all these VM's running, all identical image, and configuration....which are generally performing well...except one thing, IP acquisition.
The 13 are all identical, and some inconsistently seem to return with "limited or no connectivity" - when this happens...it pretty much trashes the VM. Rebooting or renewing IP..it's no help.
What does sometimes help, is replacing or adding a NIC. I'm normally using the VMXNET3 adapter...but have also tried a little with other adapters. These VM's are running 32bit XP SP3.
The part that is weird, so I can assign a static IP, and it seems to recover, but only appears to, it doesn't actually have any communication. Then, regardless of static or dynamic, basically the problem is that NIC1 will go to crap, so I power the VM down, remove the NIC, and power back up (to make sure the VM guest OS registers the change), then power down and add a NIC, and it still won't work. But sometimes I add a NIC2...and it will work..but only when both NIC's are present.
Sometimes when I add NIC2...NIC1 and NIC2 will work. I had a NIC1 and NIC2 that didn't work..so I added NIC3, and then suddenly NIC2 and NIC3 worked, but not NIC1.
Again, it's inconsistent...At first I thought it was VM dependent, so I was wiping VM's and recreating.
Any thoughts are greatly appreciated!
I tended to agree with your first analysis originally, which is why I had port security increased. However, at this time I've removed it. Unless MAC limits are a separate setting I'm unfamiliar with?
I also thought it strange that when the VM would have 3-4 NIC's suddenly many of them would work.
pMode came to me in the way of a technical doc on vmware support..and highlighted that individual VM's that can't get to DHCP may be resolved. It seemed to really make a difference when I implemented it...in so far as all of them quickly recovered, and I was able to remove all extra NIC's in the configuration.
My feeling is that it might be some kind of ARP poisoning going on in differences between vSwitch and pSwitch, but pMode resolves that, at least technically, by allowing all hosts to see all traffic. Though it probably puts a separate cost/burden on performance and we know it does on security.
I will try to find the documentation, I had it yesterday but didn't save the link 
I'd like the understand the issue..because pMode may fix it..but not be the right fix.