What you are describing is what happens when antivirus programs block programs that they consider to be "unsafe" or "unwanted". Note that antivirus programs usually download updates automatically and such an update can change how they handle mIRC causing it to suddenly stop running. This isn't to say it's any kind of antivirus program, but the hour glass appearing for a second and then nothing happening is exactly what happens when a program (usually antivirus) blocks mIRC from running.
Also note that just closing an antivirus program will not necessarily keep it from running. Some, such as Norton, cannot be completely stopped without either uninstalling it completely or else going through a lot of work to stop everything.
One option you could try would be to use a System Restore (if enabled) to go back to a time before the problem started and see if that solves the problem for you. Then, you just need to keep an eye out in case it stops working again so that you can get a better idea of what's causing it.
