The fact that a news article got written about a child separated from her parents, goes to show how rare it is. If it was happening on every flight, no one would be writing an article about a single incident.
On the few occasions that I've seen parents still not sitting with their children after boarding, someone has always moved so at least one parent was with their child.
People are less likely to move when (for example) mom is already sitting next to their child, and dad is trying to also move into that row. People may move, it is less likely. Especially (as happened on my recent flight), the dad is asking the woman in the aisle seat of the bulkhead (lots of leg room) to move into the middle seat of the row behind. The woman said no (nicely) and the father was still sitting directly behind his wife and daughter (where he could speak to and touch them).
On the rare occasions that you lose your selected seats, I always suggest that people try to fix it before getting onto the plane (depends on when you figure it out).
I've posted this before, but my suggestions of the steps you can/should take:
1) If there is a flight/equipment change and there are no seats together, try calling the airline. Airlines hold back some seats and may be able to open up enough so that all children are beside one adult.
2) Keep checking - people cancel flights/change seats. For people in the "single seats", choose ones that other people may want so that you have good seats to trade (i.e. aisle seats near the front of the plane).
3) Do online check in at the 24 hour mark. The seats that are held back are now opened up plus some people may have been upgraded. You have a good chance of moving to seats that are together.
4) Get to the airport early and ask the check-in agent if there are together seats that you can move to (again, people may have moved/upgraded/canceled).
5) When you get to the gate, talk to the gate agent. Changes are still happening and they may be able to help you.
6) If all else fails and you get on the plane and you have all single seats, nicely ask people if they would mind trading (but know that they have every right to reject the request). You have much better odds if you are offering your "better" seat. For example, if one seat is in row 5 and the other seat is in row 32, you'll do much better asking the person beside you in row 32 to move up to row 5 (and you and your child sit in row 32) than the opposite.
7) If you are still separated, you can choose to deplane and take a later flight. Before considering this, make sure you know if there are still together seats available on a subsequent flight.
I have NEVER seen anyone get to step 7 (not saying it doesn't happen, I've just never seen it) and rarely step 6 (generally only on holiday flights with lots of families none of whom want to sit split up or even go one adult/one child one place and another adult/child somewhere else.
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(unless the airline is going under in the next few hours).
