Are you including the protocol, e.g. http://? Do you copy and paste a working URL?

I don't understand your reference to pasting; when using Insert|Link it should create and insert the link for you, with no pasting necessary.

You could also just paste the URL directly into your message text, on the KISS principle.

Sorry about the pasting reference, I should have said Insert/link. I have inserted links with and without the protocol http://. Same result. When I type the link address into my email I highlight and copy the text, then I select Insert/link and proceed from there. Sometimes the copied text is already displayed in the link box and other times it isn't. I type the web address in the box and then select the option to 'attach the source of this link to the message.' End result is always the same...the recipients complain about the link not working.

Am I missing something?

If what you're linking to is a webpage that is accessible to anyone, then I would NOT select the "attach the source" checkbox.

When you save a webpage in your browser, typically an HTML document is created, along with a folder into which are written the graphical elements, and possibly other linked documents. You can see that if any of the linked items themselves contain links, there is a theoretical possibility of a complex and multi-layered hierarchy of documents and folders being generated.

Now, if we select that "attach" option, then it seems to me that Thunderbird needs to do something similar to what the browser does when saving a page, and frankly, I don't think Thunderbird is that clever.

You don't need to send the page's content; your correspondent's browser or mail client can get it for them.

I think the appropriate time to use this option is when the link points to an item that is not visible via the Internet, such as a document or file on your own computer or local network, and ideally it would be a single, standalone, self-contained document with no links to any external resources. So a Word document that pulled in pictures or Excel spreadsheets would not be suitable. But turn it into a pdf, and it's more likely to succeed. But in that situation, I'd send it as an attachment, anyway.