A few questions before I can help...
What program are you using?
Where are you copying the images from?
Where are you pasting the images to?
I'll go ahead & say your using MSPaint. Assuming your copying an image you've made on MSPaint, & then pasting it on another file using MSPaint:
To eliminate the loss of color problem, save your file as .png or .bmp. Now instead of copying it right away, open the other file you want to paste it to & save it as either a .png or .bmp. Now, click "Edit" & "Paste From" at the top of MSPaint & find the first file I told you to save & open it. This time there shouldn't be any color change.