We take a broad range of insurances, so usually if they leave it is not because of insurance.
I will usually ask my staff on any record release in the area if they know why the family is leaving. The staff usually knows, they often check to make sure it's a valid release. I review every fax so I know what releases come in.
Occasionally, the patient doesn't realize we accept the insurance. The others are leaving because they did not like the staff, the hours or want another opinion.
If they think the grass is greener elsewhere, I'm not in a hurry to take them back. If I like them, I might, but then again... If I don't (or the staff doesn't) then NO Deposit, NO return. They burned the bridges behind them.
It's possible the staff might have been rude, but it would have been in reaction to worse behavior on the other side. Usually I can tell, even though the parent/patient is sweet in the exam room, I can usually tell those that are saccharin vs the truly sweet people. Saccharin parents are usually not nice to staff.
I have never received a letter detailing why they are leaving. I have never sent a letter to let them know they are welcome back. I have talked to parents who are moving out the area, they are usually welcome back.