I've tried riding hands-free a few times but haven't been very successful. Like the OP, I used to be able to do it fairly easily when I was a kid. Different bike geometries must be part of the reason like others have pointed out, though my current bike is a hybrid and probably doesn't have as aggressive a geometry as a road bike...
I do find it easier to ride hands-free while I coast.
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The value of your life doesn't change based on the way you travel. - Dawn Schellenberg (SDOT)