I have a server with Softlayer, and from time to time, it completely disappears from the Internet. It becomes unreachable from anywhere. I can't ping it for a few minutes. Then it comes back. When it disappears, I'm logged in and the load is always low. When I'm able to log back in, I see the uptime is several days, so it hasn't rebooted either. From the Softlayer CP I can see there haven't been any network issue either. While the server is unreachable, I'm still able to access the Internet properly, as usual. But I can't ping this server from other servers for a few minutes every time. Then it works again. Any idea?
Sounds like your host has a routing issue or bandwidth issue of some type at these times but could be a hardware issue.
Since you have other servers I would suggest you run traceroutes when things are normal and then when the server is down. This should highlight where the problem is.
Could even be a dodgy network connection, network card or even a problem with auto negotiation on the switch or just someone going in the cab where the server is and disturbing a cable (all of which I've experienced).
You could also run mtr (on unix) to watch for packet loss and do an ifconfig (on unix) to check if you are logging an errors.