Soban,

Here are some things I think you need to clarify.  As of late I have been battleing a lot of CAD issues and calls dropping. 

1.  Are the agents remote or at the site where the CUCM and CRS Servers are located? 

2.  If these agents are remote, have you properly placed Voice QoS on all WAN and Switchport/Trunk links?  How are you prioritizing CAD traffic or are you?

3.  Are the agents actually "answering" the phone and then the call disconnects, or are the agents merely presented with a call in CAD and then the call vanishes?  IF it's the latter, then you need to pull the MIVR logs from the server for the date time ( +/- 5 mins ) and open up a TAC case with the following in mind.....

A.  CAD by default has logging capability on each of the agents machines.  Under the installation folder there is a logs and a config folder, you need to turn up the logging on CAD for the agents that are having the problem.  

On the work station open up the AGENT.cfg file and change the threshold value to DEBUG in all capital letters, if you look about three to five lines down in the agent.cfg file you will see a line that says threshold=INFO, that needs to be changed to threshold=DEBUG. You will need to right click on the file and select “open with notepad”. 

(agent.cfg file will be in c:\program files\cisco\desktop\config folder )

Once you have turned up the logging, please reboot the PC’s later tonight, once rebooted let me know. 

Now, if you can pin down an occurance of this again, then grab the agents CAD logs, and the MIVR logs and you should be able to find your culprit.

Question, are the agents being moved into the "Not Ready" state when the call stops ringing at their desks?  If so you may have a network issues ( latency, QoS, etc ), by default CAD communicates with CRS every 2 seconds using a keep alive, if it doesn't hear back from the server, it sets the agent not ready.

There are some reports you can run, but I think you should go to the logs, they never lie.

Hope that helps.

Alex