When does the mandatory minimum climb gradient during an Instrument Departure Procedure end?
I believe that now I am able to provide an answer to my own question.

I think that the "minimum of 200 ft/NM" rule applies during the whole climb phase. In other words, until the end of the SID, where either the enroute phase begins or the SID itself provides some enroute transitions as a passageway to the enroute phase.

FAA's TERPS manual clearly states:


  Chapter 2, "Sloping OCS" 2-1-4b. The concept of providing obstacle clearance in the climb segment of an IFP is based on the aircraft maintaining a minimum climb gradient. [...] The minimum climb gradient that will provide adequate ROC in the climb segment is 200 ft/nautical mile (NM), unless a higher gradient is specified.


In addition, the rule is also repeated in the PBN manual:


  Chapter 1, "Common Criteria" 1-3-1g(2). Climb Gradient (CG). Obstacle clearance in a climb segment is dependent on the aircraft maintaining a minimum CG to a specified altitude. The minimum CG (also referred to as standard CG) is 200 ft/NM.