I am seeing something similar, but only with two hosts. They show down/up on what is seemingly a random pattern. The down/up emails are about 5 minutes apart when it happens. They are both domain controllers. They are VMs on hosts with many other VMs, so I know the network isn't going down, otherwise I'd lose them all at once. Also the host servers are monitored and they never show down. It's just these two DCs. They are Server 2012 and we have other Server 2012 VMs. I tried running snmpget from the CLI like the FAQ suggested, but it returns fine with no errors. I've even had Observium tell me these DCs are down when I am in active RDP sessions to them.
My gut says Observium is not to blame since only these two hosts are effected, but I don't have a lot of experience troubleshooting SNMP. I've been digging through the event viewer on the DCs trying to find a cause, but so far no luck.