It is advisable that you purchase the visitors insurance before the trip starts and keep the insurance for the entire trip.
We recently got a phone call from a customer who just purchased the insurance and wanted to change the effective date from the next day to the same day. When asked why he wanted to do that, he initially protested and hesitated about why we are even questioning him. After some discussion, he revealed that his mother is already in the hospital now.
It seems that his mother arrived 2-3 weeks ago, and when she was hospitalized, he hurried up and bought the insurance and later realized that it only started from the next day. Therefore, he wanted to change the effective date to today to cover the hospitalization that already occurred.
Obviously, no insurance company (that sells any kind of insurance anywhere) can afford to just give away money to people who need to claim. No company can stay in business like that.
When asked why he didn't purchase the insurance so far, he said that he thought that the visitors insurance can be purchased instantly online and can be made effective right away. Therefore, he didn't feel the need to purchase earlier.
He continued to argue and request and he also said that "It seems you are Indian and I am also Indian. Therefore, can you do something on that basis?" Obviously, nothing can be done about it. His only option is to pay out of pocket at this point.
Had he purchased the insurance before she arrived into the US, that hospitalization might have been covered. But at this point, it was too late.
The basic logic of insurance is that many people pay the small premium and if few people need large amounts unexpectedly, insurance company will pay them while covering their expenses and profit. If only people who buy the insurance are the ones who need it, there is no way to provide large sums of money to all of them.
I hope this would help others in making the right decision to get proper coverage for their visiting families.