What are acceptable circumstances for changing flight tickets? Would illness qualify?

You can almost always change the dates or times of your flights, but you will also almost always have to pay some kind of a fee and possible fare differences, regardless of the reason for the change. People get sick all of the time, but the airlines don’t waive the fees. If they did, then everyone would plead illness as a reason to avoid the change fees.

However – it never hurts to call them up and plead your case. It probably won’t make a difference, but you never know.

The only way to avoid change fees is to buy a full fare, non-discounted, fully refundable ticket. If you did that, then you should be OK, but few travelers do that these days.