Hmmm.. I just added updated an entry with a link like this:
<a title="My Link" href="http://connections-pro.com" rel="nofollow">link</a>
And it worked fine.
Now, it’s possible another plugin or the theme is hooking into the core WP sanitization functions which Connections uses to prevent bad things is stripping the links. The WP sanitization has a whitelist of permitted tags and their attributes, this whitelist can be altered by plugins and themes.
If this is the cause, the only way to find out is to deactivate all other plugins temporarily except Connections and cMap then edit an entry to see if the link is still stripped. If it isn’t then you know the cause is another plugin. What you’ll have to do is activate the plugin one at a time until the issue comes back. When it does, the last plugin activate is the cause.
If you deactivate all the other plugins and it still happens, then it’s likely the theme is the cause. Rather than changing themes to try, if you grant me a temp admin account, I’ll login and remove the sanitization from the bio field, temporarily, which will basically use whatever is entered in the field as is without any safety net. This will allow any text/HTML to be displayed. If it works after that, then it will have to be the theme that’s the cause. After that’s established, the sanitization will have to be added again, but at least you will know why it is happening and the cause.