Your parents will get a vist visa upon arrival at Doha airport for a one month stay, if they want to stay longer than that they only need to go to the immigration office at the airport and extend they visa, they will get another 30 days. (QR100) There is no further renewal after that, so they do not need to fly out of the country after expiry of first visit visa. Only after expiry of the second visa if they wanted to stay longer than two months. Then they can fly out and return and start the same process.
Your parents will get a vist visa upon arrival at Doha airport for a one month stay, if they want to stay longer than that they only need to go to the immigration office at the airport and extend they visa, they will get another 30 days. (QR100) There is no further renewal after that, so they do not need to fly out of the country after expiry of first visit visa. Only after expiry of the second visa if they wanted to stay longer than two months. Then they can fly out and return and start the same process.