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As a beginner, you have to be careful of over-practicing if you're having difficulty achieving a goal. This really goes for any level. Once frustration starts to set in and mistakes are continuously being made, then you have to unlearn those. If you're having difficulty, set the guitar down for a few minutes, and hour, or a day. Your brain is processing that information even if your guitar is not in hand. Let your muscles then attempt the music when they are fresh and haven't become tired and strained.
Oh hey, that 2min thing sounds like a really good idea .. probably enough time for a mental breather as well. Sometimes I feel like I just have to keep on doing something and doing it over and over continuously till it's right and that's often counter productive in so much as I get tired and then don't focus, or I get sloppy about whatever instead of really improving >.<
I get like that...but my own cure is to swap out to new strings. When you do this, you are stretching them, tuning, restretching, retuning...checking out the harmonics, maybe tweaking the bridge. Eventually, yer playin'...
"Feel what you play...play what you feel!"
Sorry, I know you're gonna hate this but my recommendation is just to practice more and more. It's one of those annoying things that will gradually get better over time. It's not something you can sit down and nail with a single practice session.
I think it's a matter of enjoying your practicing... so whatever you can do to make it fun and relaxing at the same time. If you like to sing, or even if you don't, try singing along. This will take your mind off your fingers and you won't be so critical of yourself. Perfection will never come. But if you keep plugging you'll get closer and closer. Right now it's about putting in the time.