no signal input

After I have been away from my computer for a while, the monitor blacks ou as it should, but some times when I come back to it, a movement of the mouse will turn the monitor back on. However, I have been receiving a message “no siganl input, or cable disconnected or lose”. If I turn the monitor on, I get the colored lines and have to use my reset button. This is not a problem unless I am downloading something, and then I lose everything that has been downloaded to that point.
How do I correct this, so that when I move my mouse the monitor turns on and the Desktop appears, or the downlaod appears.
Thanks