This is because your skeleton document is a template for you, not for Writer. Technically, a template file has extension .ott, not .odt (middle “t” stands for template, middle “d” for document and final “t” for text).
You can of course open your .ott with a double-click and Ctrl+S or File>Save (As) takes care not to overwrite it by changing the extension to .odt. However, with this workflow, you don’t change default save behaviour which is in the same directory as the initial document.
To get what you’d like, your user .ott template must be “declared” to Writer so that it is stored among the other templates (more sophisticated schemes are possible, with multiple template directories, but you seem to be a newbie, so start with simple things). You do that with the various items in File>Template.
First step is to use Save as Template. Then use Manage Template to designate your preferred default template.
You seem to be working under Windows. There is a bug in this OS with regard to creating new documents. Don’t do it with the OS New Document. It creates an empty file which will not be attached to your user template. Consequently, always create new documents from inside Writer.
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