It is not common for projectors to shut off due to a worn out lamp, but I could certainly think it is possible. You know the lamp is worn out. The only way at this point to know if there is some other problem is to swap the lamp.
yeah ,yhen you can caculate the exact time .Take a note of your hours (if you wish to know total useage) and re-set your timer to zero..
That should get rid of the warning notice and may stop the shutdown problem..