Hi Claus,
Responsibilities are a little unusual. They represent a kind of 'rule container', and are linked to one and only one rule, you cannot have multiple rules pointing to the same responsibilities.
The link is provided by infotype 1240. If you're feeling adventurous you could try writing a report to relink them to the new rule. A word of advice is not to do this directly in the table (HRP1240) but using the proper infotype operations. This will delimit the previous one and create a new assignment as of a specified date (today). More traceable and easier to reverse if something goes wrong.
Please note that I have not done this myself, nor is this a SAP-sanctioned approach (not that I know of anyway)...
Let me know how you get on. 
Regards,
Mike
Edit: Was a bit curious about this myself so had a quick look (7.4). It seems that the responsibility itself (IT 1218) also contains a reference to it's rule. So you should probably update both.
Another often-overlooked feature of the responsibility editor is the table view (table button). Doesn't let you add, but sometimes more manageable view if you have many responsibilities.