We have a Miele G 870 SC dishwasher. The soap dispenser always opens properly to dispense soap if we run the Economy cycle, but it always stays closed if we run a Normal or Intensive cycle.

SOURCE: Dishwasher soap dispenser won't open during cycle

both have a wax motor on them that needs to be replaced you just remove the panel and replace the wax motor is what its called

SOURCE: soap dispenser

A wax motor controls the opening of the lid. Also a seal that fits around the latch lever may be deteriorating and obstructing the function of the lever. Follow the link below for images and part numbers with cost.
Item# 1405...$20.30
Item# 1434...$ 3.95


http://www.repairclinic.com/SmartSearch/smartsearch.aspx

SOURCE: Dishwasher soap dispenser won't open during cycle

I had the same problem with my GE Adora. The dishes were getting cloudy and the soap dispenser would not open. Turns out the hard water deposits were causing the soap dispenser to stick shut. I purchased and used Dishwasher Magic which is a dishwasher cleaner designed to remove limescale, rust and buildup. I used as directed and now my dishes are sparkling and the soap dispenser pops right open.

SOURCE: soap dispenser does not open during wash cycle

• Hi,
  
  
  please try this...
  imer:
          On mechanical set ups the timer is attached to the detergent cup by an actuator arm. This arm is usually plastic, and if it is broken or otherwise defective then the detergent cup wont be opened. Check the linkage to make sure it is functioning correctly.
  Bi-metal switch or wax motor:
          The bi-metal switch is simply a very precise device that warps, bends, or otherwise deforms when power is supplied to it. The timer operates the bi-metal switch, which inside the dishwasher door. Then the switch is supplied with power and it is working properly, the bi-metal switch deforms away from the latch holding the detergent cup closed and the cup opens dumping the detergent into the washer.
          Some dishwashers have this switch wired through the motor power feed or the heating element. If they are defective then the detergent door will not operate correctly. If the switch itself is defective then you will need to replace it. Another type of mechanism is a wax motor. Wax motors are sealed units filled with wax and found in newer dishwashers and work by heating the wax and forcing up a piston which in turn mechanically opens the detergent cup door. This type of device is also controlled by the timer.
   
  Detergent cup:
          Sometimes the detergent cup becomes built up with old detergent that prevents it from opening correctly. It's usually a simple fix to clean this out. If cleaning it is impossible then you may need to replace the cup assembly.
  
  please rate my suggestion..
  

SOURCE: Dishwasher soap dispenser sticks

Your soap is clotting because there isn't enough water being sprayed around inside.  The water spray washes the soap out of the dish, if all is working well.  My machine had the same problem.  I had sufficient water level, but the spray head wasn't spinning very well.  I found the end-most hole in the spray bar to be plugged.  It is the end hole that provides a jet that makes the head spin.  I cleaned a bunch of debris out of the hole and the mchine started working and cleaning like it was new.  That was quite an axccomplishment since the machine is 15 years old.