What are the other security applications running? What is the RAM of the computer?
Open your taskbar (Ctrl+Alt+Del) - Process Tab
Then open CIS from try icon and see memory alterations of other programs to see if any other program is interfering.
I hope you do not have two real time Antivirus or Antispyware applications monitoring the computer. In that case this type of problems can occur.
The only other security software I have is Avira AntiVir Personal (free edition).
I think this problem only occurs when a new software is initiating. The alert box prompting me for a response should pop up immediately but for some reason it doesn't, and Comodo become unresponsive. The alert box only comes up 2 or 3 minutes later, and when that happens the taskbar icon is responsive again.