Almost all good putters will tell you the same thing: having your eyes over the ball is important to holing more putts. Although the all-time greats of putting may have had differences in their posture or tempo it's truly fascinating (and telling) that all the greats maintain this common approach of keeping their eyes directly over [or slightly inside] the ball at address.
So how does it help? Well, getting your eyes over the ball will not only help the rhythm of your stroke but will also decrease the chance of opening or closing the putter face at impact. And for those tricky, shorter putts getting your eyes over the ball aids in maintaining the correct back-to-front stroke that will help start the putt on line. But what's the best way to make sure you are aligned correctly?
For me, I use one simple drill prior to my round on the putting green. I line up a 4 foot putt, address the ball as if i were about to hit the it and use one hand to drop a ball mark from the bridge of my nose straight down. If my eyes are over the ball, the coin will simply fall and hit the ball. Once I've confirmed I'm in the right position, I go ahead and practice hitting those 4 footers.
Try doing this a few times on the practice green prior to playing. Once you've made sure your eyes are over the ball, the putting stroke frees and you will be able to hole more putts.