The MSDN site only states:
CONNMGR_STATUS_CONNECTIONLINKFAILED The connection link was prematurely disconnected.
There is no further description. I assume you have a problem with your provider. Beside from that, I do not rely on Connection Manager (CM) connections. Soemtimes it states a connection is available, but it is not in real as CM uses a cached information.
Normally, for getting a connection, you only have to issue a http request. CM will choose the right connection. Usa of CM API is only usefull if you need to switch between different connections with same destination network. But this i normally not the case, as you will have normally only a WiFi and one GPRS connection to internet and WiFi is selected prior to GPRS (due to costs).
What is the scenario that makes you think you have to use CM?