Should I remove veneer from an antique sewing machine? Its peeling dry

It depends on what you are doing with it. You could devalue it if you remove the patina although I am not sure what the market is for old sewing machines. You could spray/seal it with polyurethane to prevent any further deterioration. You could also sand it and repaint if you intend it as an art piece.

it really depends on what is more important to you. Are you going for looks? Or is the value worth more to you? I am a quilter and I LOVE vintage things. I have a sewi g machine that has the finish that's coming off and everybody that I talked to all said the same thing. If you refinish it, it will bring the value of the sewing machine downwhite a bit. However, if you refinish it, it can look like a much more attractive piece of furniture. Just make sure that you take it to a person that knows what they're doing.

Why not try oiling it first to see if you can rejuvenate it.

If you are wanting the original look there are several ways to go. If all the veneer is still there it can be re glued. If some is missing you can buy veneer and fill in the missing pieces. It is easier to cut the remaining jagged edges to straight edges. If you are going to paint you can use wood filler and then paint.

I agree that it would depend on the sentimental value as well as the true value of the piece. I would go with trying to restore the veneer as it's really not that hard to fix. Here is a link that may help with restoring veneer: http://home.howstuffworks.com/home-improvement/home-diy/furniture-restoration/how-to-repair-wooden-furniture-veneer.htm