Working in support, I've noticed a common problem the LEM encounters when running in Hyper-V is this:
If the Hyper-V system initiates a failover, migration or something else that causes the LEM to halt abruptly, when the LEM comes back on-line it won't be reachable on the network. Even if the LEM can be accessed via the virtual console, it's unpingable and, more importantly, agents and syslog devices cannot reach the LEM to send data.
I've had a few of these cases recently, and the issue seems to be related to an option that Microsoft included in the Hyper-V console: dynamic MACs. I'm not sure why this is a feature, or why it's the default setting for a new virtual machine. What I have seen is that if the LEM reboots and gets a new MAC, it treats that as a new network adapter. Since the LEM isn't really meant to have more than one adapter connected to the corporate network, if it chooses to connect to this adapter, it's connected to nothing, and unreachable.
The way to avoid this problem is to assign a static MAC, meaning that if the LEM suffers a hard shut-down, it doesn't come up with a new adapter the next time it boots.
If you really want to dig into it, this is a result of the write_net_rules library in Linux:
And the dynamic MAC causes multiple entries in 70-persistent-net.rules file when the LEM (or any Linux system using this library) gets a new MAC.
And MSDN Blogs has some good entries on Dynamic MACs: