What causes a dryer to not stop itself after a load finishes?
If it keeps running, the most likely problem is a restricted air flow in the ventilation system. This problem won't necessarily make it stay on forever, but it can drastically increase your drying times to the point it feels that way. The same issue can arise if your blower wheel becomes clogged with lint, small clothing items, etc. As stuff can escape your lint trap and fall down into the blower wheel, taking proper care of your lint after each load is vital.
A completely different scenario could be playing out if you have a gas dryer. These machines contain gas valve solenoid coils which can stop working properly. As a result, it's possible for the burner it fuels to no longer produce sufficient heat. It's best to replace an entire batch of coils if any of them are discovered to be faulty.
Another possible cause is a shortage in the heating element. You can test with a multimeter to see if there is continuity. If not, a new element is needed. Your dryer will keep trying to finish drying the clothes indefinitely if the element never heats up properly in the first place.
Sometimes the cycling thermostat is to blame. This thermostat is responsible for kicking the heating element on or off depending on the temperature inside your dryer. If it's not working right (check for continuity) it will need to be replaced with a new one.
One more, but rarer, potential reason for a dryer not stopping is because the moisture sensor isn't working right. A defect in this sensor will tell the dryer that there is still moisture in the clothing and, because of that, it would keep feeding heat to the dryer.
Just bought a new dryer? We recommend you swap out the vinyl tubing, if included with your machine, and install aluminum instead. Unfortunately, vinyl tubing poses a more serious fire risk while aluminum is considered fire-safe by federal standards. Next, make sure the machine is placed evenly on the floor in your laundry room. You might need to adjust the legs to get it balanced out, especially if your floors aren't level. The machine should be sitting completely flat, otherwise it can easily rock back and forth which will cause extra wear and tear all over.