I have an eclipse, and a "group of one object". when I try to punch the two, it does not work. Rather, it turns that "group of one object" into a compound shape. I tested the eclipse with a rectangle, and did a "punch", and it worked fine.
It's not clear what your question is, what the problem is, or even what you're describing. A screenshot of the canvas and the Layers panel might help to clarify.
If you're using the Properties panel's Boolean operations to apply the Punch command, a compound shape is a desireable and expected outcome. (And it seems to work on both vectors and groups.) If you're looking for a composite path instead, you can click the Combine button (also in the Properties panel) to convert the resulting compound shape into a composite path.
Using Modify > Combine Paths will give you a composite path instead of a compound shape, but it cannot be applied to a group.
Try one of the Boolean operations in the Properties panel to get the effect you're looking for. If this doesn't work, it might be because the "Group of 1 object" contains a bitmap and not a vector. (You cannot apply a Boolean operation to a bitmap.)
BTW, unless you've applied a style or effect to the group, there's no reason to have a "group of 1 object"; you could use the Ungroup command on this object to make things simpler.
Double check what you've selected before you run the Punch command: Is it only the Ellipse and the Group of 1 Object?
According to the alert, one of the selected components contains subpaths of a compound shape. Perhaps this is your Group of 1 Object. As suggested previously, you might want to ungroup this object so you know what you're working with. In fact, this is what I'd suggest. If the group contains a compound shape, try selecting it and using the Combine button in the Properties panel to convert that shape into a Composite Path. From there, you should be able to reselect your original two elements and apply the Punch command.