Just to expand a little on what Paddy has already told you, It sounds to me like you have been running certain applicationbs directly from the disk image. This is usually OK, but just like a real physical disk, if it is removed from the computer, the application goes with it. The best way is to follow Paddy's advive and save the application to your hard drive, and run it from there. After, you have done that, you can then delete the .dmg if you want.
Steve