The biggest reason weekend golfers so often three putt 30 to 40 foot putts is they simply don’t practice them. Because of this they haven’t developed a feel or “touch” for putts of this length. They end up hitting the ball and hoping rather than stroking the putt with a level of confidence.
Great putters through regular practice have developed a keen sense of feel for longer putts. They also have set a more realistic goal of leaving the ball close enough to the hole to have a short second putt rather than thinking about making the first putt.
When confronted with longer putts I would first recommend visualizing a larger target. Imagine a three foot diameter circle around the hole, and then focus on leaving your first putt within the circle. If successful the longest putt you’ll be left with is 18 inches.
On longer putts stand slightly taller at address and make a longer stroke with more relaxed hands and wrists. This allows you to sense and feel the acceleration and release of the putter head. Also before each long putt make a number of practice strokes to help sense the length of stroke and pace needed for the required distance.
An excellent drill to help you develop your feel is after making your practice strokes to close your eyes just before beginning your actual stroke and keep them closed until the finish of your stroke. You'll be surprised how this enhances your feel and touch.
Make sure to include longer putts in your putting practice regiment if you’re not already doing so. With continued practice you’ll see far fewer three putts on your scorecard.