The general rule is that they will not cover any pre-existing conditions, so the time to take out insurance is when the pet is healthy.
I insured one of my cats shortly after I got him (at 12 months old). At the time he was quite healthy. He passed away 7 months later having run up a vet's bill of 2,500 euro - luckily he was covered, so all I paid (apart from the premium) was 2 excess charges of 60 euro. All blood tests, x-rays, and medications were covered without question.
I'm not sure what might have happened at renewal time, if they would still have covered the pet for the particular condition (he didn't live that long).
I was certainly very grateful for insurance for that pet!