The solution is to stop trying. No really:
The first thing to do is isolate the passage. Take as much time as you need to allow the left hand to comfortably reach the target. There are two more things you need to do next: make sure your eyes are consistently watching where the left hand fingers are going rather than the fingers themselves. In other words, look at the fret board, not your fingers. The second other thing to do is think about the left hand fingers pressing first before you play. This sounds simple, but it is a very good tip. I think of the simple and easy tips baseball players get: "Choke up on the bat." "Keep your eye on the ball." Well, we guitarist have one of those sayings too in a situation like this: "Press first, then play." At the 3rd fret, make an extra effort to make sure the left hand is pressing before the right hand plays.
Take all the time you need to get from the 12th to the 3rd fret and get as comfortable and relaxed as possible. You really need to make this pause in between the frets take as long as needed for now. When in doubt, make the pause LONGER and not shorter. Imagine how easy and comfortable that section at the 3rd fret would sound if you just started from right there? Actually, don't just imagine it. Pick up your guitar right now, and start right there on measure 4 discovering how good and easy it feels. Next:
From this point forward, never play that third fret section again until you've given yourself as much time as needed to get that same level of comfort described above. Embrace that big pause; it is now part of the piece. And remember something I say (and we all hear many times): for better or worse, we are creatures of habit. When we do something over and over, we are going to get very good at it. In this situation you are speaking of, it is common for us to get really good at playing a section poorly as we try harder and harder. Our bodies learn nothing but tension. The harder we try, the worse it gets. So just stop trying. Do the complete opposite. Those great feelings of relaxing and adequately preparing the 3rd fret will become habit. And with more practice, the habit will become stronger. And finally without trying, the time it will take you to get from the 12th fret to the 3rd fret will significantly diminish. That pause will become shorter without effort.
Are you ready for the icing on the cake? Only after you have this well established and have only a small pause going from the 12th fret to the 3rd fret, you can make it even better! Begin slowing down at the end of measure 3 at the 12th fret. This sets the listener up to expect to hear the 3rd fret a little later. And, you can effortlessly deliver! Even if you COULD seamlessly get from the 12th fret to the 3rd fret (and I just showed you how to do it) you probably wouldn't want to. Imagine a singer making that leap. It takes time to get down there. (Yes they can do it without taking the extra time, but it doesn't sound fitting). Taking some time there is a very musical thing to do. And to make it sound great, you begin slowing down at the end of the 3rd measure. That sets you up for a very comfortable, natural, musical 3rd measure. And finally, you can even foreshadow this a bit in the first 2 measures of the piece.
Best of all, you will find many other places to use this advice!
Dr. Todd Tipton, Noda Guitar Studio
Charlotte, NC, USA (available via Skype)