VMware KB article 1022751 lays out the details of an interesting bug in ESXi 4.0 and 4.1 pretty plainly:
When trying to team NICs using EtherChannel, the network connectivity is disrupted on an ESXi host. This issue occurs because NIC teaming properties do not propagate to the Management Network portgroup in ESXi. When you configure the ESXi host for NIC teaming by setting the Load Balancing to Route based on ip hash, this configuration is not propagated to Management Network portgroup.
(Note that load balancing by IP hash is the only supported option for EtherChannel link aggregation.)
Unfortunately, the KB article’s workaround – there is no patch that I’m aware of – requires network connectivity to the host via the vSphere Client. But what do you do if you’ve just sawed off the branch you’re sitting on network-wise, and can no longer connect with the vSphere client?