'Every now and then' should either be at the start of at the end. Every now and then, my washing machine broke down. My washing machine broke down every now and then. Single word adverbs (often, sometimes, usually) can be placed between the subject and the verb, but this is not usually done with multi word adverbs (every now and then, from time to time).

The sentence you provided is almost natural, but it would be more correct to say: "My washing machine every now and then breaks down." This sentence is in the present tense, which is appropriate for describing a recurring issue with your washing machine.

I think the original sentence is not unnatural by itself, but I usually hear this sentence with the action before "every now and then" or with "Every now and then" at the beginning. Like: "My old car would break down every now and then" "Me and my friend used to sing together every now and then" "Every now and then, the cat likes to walk inside the house"