How do I keep individual objects, each a different color, from changing to a single color when I duplicate or group?
It is an SVG file in Inkscape
This is a purchased file. When I group, duplicate, or print the colors of the individual letters change to a single color.
It's hard to say what's wrong without being able to analyse the SVG. There's no telling how it may have been constructed.
It might be easier to just recreate something like this in Inkscape from scratch. It could easily be done in a couple of minutes and would avoid the problem of trying to fix someone else's artwork.
All you need is a photo of a leopard skin, duplicated as many times as necessary, and some filled rectangles and some text with the fill set to white. Group the images and rectangles (but not the text), then select everything and do Object > Mask > Set. After this has been done, you can duplicate it as often as you like without any colour changes.
An example
