Until you can get this sorted after the first rinse toss in a dishwasher tablet. Set the kitchen timer so you'll know when to do that after you start the load. Call frigidaire directly many times they will send the parts for free. There is a 1 year warranty on the product.
On many dishwashers, a plastic actuator arm mechanically links the timer to the detergent cup. When the timer reaches the proper time in the cycle, the timer activates a lever that opens the detergent cup. If the linkage is broken or defective, the cup stays closed after you've closed it. Check the link and repair or replace it, as necessary.
Bi-metal switch or wax motor
A bi-metal switch is a simple electrical device that deforms when electricity is applied to it. The degree of this deformation can be engineered to concise standards.
The timer energizes the bi-metal switch inside your dishwasher door--directly behind the detergent cup--when the detergent cup should open. When energized, the bi-metal switch deforms away from the detergent cup latch, which opens the detergent cup. If the bi-metal switch is defective, it may not deform enough to open the cup. If that happens, you need to replace it.
On some dishwashers, the bimetal switch is wired through the heating element or motor circuit. If the element is broken (or open), or if the motor is drawing low current because of a low-fill situation, the bi-metal switch doesn't open properly.
Newer dishwasher models use a wax motor instead of a bi-metal switch. It's a sealed unit with wax that heats up and pushes a piston through to open the door. The wax motor, controlled by the timer, mechanically opens the door.
Detergent cup, itself
The detergent cup itself can become clogged with old dried detergent that prevents it from opening. Sometimes just cleaning the cup takes care of the problem. If not, you probably need to replace the entire cup assembly