You could try going to:
Creating a file called run.bat and editing it in notepad to contain the following contents:
java -jar client.jar
Then execute the bat file directly. It'll open the client w/ console on the side printing out constant information. There's a possibility that the disconnections aren't caused by your network, but rather some error thrown in the client. This helps check that out - if it is true or not. When you disconnect, you can check the command prompt window. There's a possibility it'll have some sort of a stacktrace in it, pointing an exception of some sorts.