It is likely that you're trying to purchase a domain that Shopify does not support if the domain is available elsehwere, but not through the Shopify admin. While it is only a select few domains that can not be purchased through Shopify, it is almost always a domain that is regional (has regional ending such as .de). If you can share the domain you're trying to purchase then I can do some digging into what I can find out for you.
Some regional domains such as .com.au can not be sold through Shopify and will require that you purchase the domain through a third-party domain manager such as GoDaddy. You can follow our guide here on how to connect your domain once you have purchased the domain through a third-party domain manager.
I have a similar problem. I originally bought the domain from Shopify, then I deleted it and closed my shop. When I reopened my shop, the domain was still available, but Shopify shows that it is unavailable. Therefore, I had to choose a similar domain name for the time being, but, now that I am ready for a full launch, I need my original domain. How can I get access to it again?
How long ago did you purchase the original domain? Was it within the last year or longer than that?