just bumping this in case anyone has any options.

thanks if you read it, really at my wit's end at what to do with this program.

I don't really think this is the case, but if you're logged in on any other device (smartphone etc), your status might get messed up even if you haven't been on the other device in ages

That's very interesting... I've heard of and seen something similar, to this before, however, it was vice versa. They were stuck Online with their phone, even when offline but had control over their status on their computer.
Now, when you're appearing as "Offline" are you still able to get messages and calls and the like? If so, it sounds more like stuck on "Invisible."
A few thread posts I've found.
* "Another reason that your client might not be able to access Skype's network, and consequently not allow you to leave offline mode, is that a firewall is blocking Skype's outgoing communications. It could be the software firewall on your computer, or the network firewall. You can set your software firewall to not block Skype through your control panel, but you will need to get your IT staff to change the settings for a network firewall."

* "ruwim wrote:
Try first to reset all Skype settings.

Quit Skype or use Windows Task Manager to kill any Skype.exe process. Go to Windows Start and in the Search/Run box type %appdata% and then press Enter or click the OK button. The Windows File Explorer will pop up. There locate a folder named “Skype”. Rename this folder to something different, e.g. Skype_old.

If you are on one of the latest Skype versions (>6.3), then do also this:

Go to Windows Start and in the Search/Run box type %temp%\skype and then press Enter or click the OK button. Delete the DbTemp folder.

Restart Skype.

N.B. If needed, you will still be able to re-establish your call and chat history. All data is still saved in the Skype_old folder."

This one particularly seems to have solved the issue for a few ppl.
There was an old button under "Privacy" where you'd click like "show my status on the web" but that feature has since been disabled so it can't be that. I hope that you're able to get it sorted out!