I think my insurance company is pretty lenient but my agent is a jerk.
I had a time when I was late making a payment and she was pretty abusive about it even though I was offering to pay right away.
I've talked to many people in business who were frustrated about a payment being past due but until then everyone I met was 100% cool after I told them it was a mistake and payment in full was immediately forthcoming.
I've been thinking about changing my insurance but there are numerous features about my house that make it hard to insure, such as the fact that it doesn't have central heat. (I've got the same propane heater you see in many anime and also two wood stoves though.) It is coming up in February and maybe this year I will look for a new agent.