Categories of aircraft (A,B,C,D): Is it possible for an airplane to move into a different category?
The FAA's Instrument Procedures Handbook, Chapter 4 has a good explanation of this (emphasis mine):


  An airplane is certified in only one approach category, and although a
  faster approach may require higher category minimums to be used, an
  airplane cannot be flown to the minimums of a slower approach
  category. The certified approach category is permanent and independent
  of the changing conditions of day-to-day operations.


And:


  A pilot must use the minima corresponding to the category determined
  during certification or higher. Helicopters may use Category A minima.
  If it is necessary to operate at a speed in excess of the upper limit
  of the speed range for an aircraft’s category, the minimums for the
  higher category must be used. For example, an airplane that fits into
  Category B, but is circling to land at a speed of 145 knots, must use
  the approach Category D minimums. As an additional example, a Category
  A aircraft that is operating at 130 knots on a straight-in approach
  must use the approach Category C minimums.


In other words, the aircraft's "certified approach category" never changes. However, for operational reasons a pilot may use a higher category's minimums for an approach, but never a lower category's. One possible scenario would be if the flaps are inoperative and the pilot can't slow the aircraft to its normal approach speed.