You can only have a limited amount of business partners of a specific type. You can see the current limit when you try to add a new business partner.

In addition there is also a limit on how many business partners you can have overall:

You can see your current global Business partner limit in the trade center.

• Click on the "trade center" button to open the trade center
• Click on the "business partner overview" button to enter the business partner overview
• You can see the global limit on top of the screen now
  

You can increase your business partner limits with certain researches.