If you have no idea when you are going to return, guessing could mean you lose your return ticket. You could try to call if you want to extend your visit, but the airline may not always honor your return ticket on a different day. Some are more than willing to work with you, but if there are no flights or seats when you want to return - if different than your original date - you may have a buy a new one way airfare to get home. That is going to cost you. When you have someone in your family that lives far away, but is also having health problems, you may want to fly out to see them and help care for them. In this case, getting one way airfare is the best idea.
11-03-2008