This has been happening quite a bit lately... I put in a cd, after several minutes of the machine whirring and the cd working fine, the whirring stops and whatever I am doing with the CD immediately stops (it is very annoying when I'm installing something) and I get a message saying there is no disc in the drive. After about ten seconds, the disc starts whirring again and it starts up again ( I usually have to re start my installation progress ).
If anyone can tell me why this is happening and/or how to fix it please let me know.

The disc will stop spinning because it can't read anything.
Try cleaning the lens with a CD cleaning disc. (Also make sure the CD surface is clean!)
If that doesn't work it could be a sign that your laser is dying.
Is it a CD rdr only or a DVD/CD and do you have another DVD/CD drive to try it in?