I'm far from the 50's bunch (only 20) but I'll drop a comment anyway..
make sure your handlebars are true with your wheel. I hadn't ridden no hands since I was 15 before I got the bike I'm currently on. For about 3 months I couldn't do it. As soon as I took my hands off, the bike would begin to sway left or right, attempting to balance it only caused it to swing the other direction. After a while, I figured out what it was.
The handlebars didn't line up with the front fork. They were tilted at about a 5-10 degree angle. This caused the bike to be unevenly balanced and have an "odd" center of gravity. The first time on the road after correcting the problem... no hands unless I wanted them on.