I am having this problem with my 10 years old LG Top Loading washing machine.
In a normal wash cycle. It washes them it turns itself off. Then I could start the rinse cycle manually, it will do the rinse process and then turn itself off again before the spinning cycle. Then I could start the spinning cycle again.
I am not sure whether it is worthwhile to repair the machine or get a new one. Any help in finding the cause of the problem is greatly appreciated.