Are you using any router or connecting directly to computer? I use a router and my connection also disconnects automatically, then connects automatically after sometime. But, when connected directly, it works well..
Yes their connection sometimes go away. Faced this problem several times, esp most irritating during saturday evenings after 8pm when my cablewalah shuts shop & the connection is gone with "no connection to server" over the IPConnect. They are closed for sunday & so connection won't return till monday!
They told me its due to problems at their end, the switch in the nearby lamp posts from where the connection comes is faulty & goes away with overheating. During weekdays they would correct it immediately. At your end unless you have router problems you are mostly helpless.