There was a point in time where I couldn't make a putt inside of 4 feet. I stunk. It frustrated me so much because I was a good ball striker and I struggled to post low scores because of my putting. So I worked my way out of this slump. Here are a few things that helped me increase my make probability on short putts:
I really focus on my alignment now and very rarely give up the hole: I make sure the putter head is square, and the middle of the putter is addressed at the middle of the ball. I play any break by keeping it within the hole (aiming within the edges of the hole).
I am hitting these short putts a little more firm. This correlates with point 1 above; if you are aiming within the hole, you need to make sure it is a firm putt to remove any break. Hit it to the "back of the hole!"
I say to myself "straight back, straight through" at address and then execute that exact action as best I can.
These 3 points have been great for me. I try to practice this as much as I can when I am working on my putting. Give this a shot if you are struggling with the short putts.