Can I disable the sleep mode for a specific application so that my mac won't go on sleep until the app is closed?
If you have any interest in running shell script the following will work. Just set the "Display_Sleep_Time" and "System_Sleep_Time" as you want them to be along with the "App" you are choosing to prevent sleep on. By launching the script anytime you run your app your all sleep times will be turned to 0 preventing both your display and system from sleeping.
NOTE: WARNING THIS SCRIPT DOES CONTAIN AN INTERNAL LOOP. You may prefer to utilize the following script inside a Daemon rather than use the internal loop the script provides. However, the same concept applies.
You could also add a line like this to a crontab:
caffeinate and pgrep were both added in Mountain Lion.
You can get a list of power assertions with