Ok... so actual real advice. Let me see here.... if you need help with your breath control aka "breathing properly" or from the diaphram ... here's my memory of an actual lesson from my private voice lesson days.
First... lay on the floor on your back. Yes... get down there ON YOUR BACK on the floor. Put one hand on your chest (like you're gonna say the pledge) and the other on your ribcage (on the side ... thumb down fingers up... it's a bit uncomfortable, but you should get the gist). Now, you're going to just breathe normally. Don't think about your breathing just breathe and pay attention to what's going on. What you should notice is that your chest is not heaving up and down (that pledge hand on top is staying pretty stable) ... but instead your ribcage is moving in and out (that side hand is moving with your body). This is the "proper" way to breathe. Your belly is not really supposed to move. Some people think you are supposed to "breathe from your belly" and your belly should be expanding and contracting... NOT TRUE. Your lungs are NOT located in your belly, they are located in your ribcage. read edit below if you don't agree with this... TUBA do you have any advice to add in here? Practice deep breathing for a little while on the floor.
Next... stand up (slowly... and even slower if you had a few beers before laying on the floor!! 
) ... place your arms out in the air palms up (like on the Titanic "I'm on top of the world!") ... gently ease your arms down to your side KEEPING your posture as it was with your arms out in the air. This is the "correct singing posture" ... you should now feel like your shooting your chest out there for the entire world to see (oh yeah... look at that chest... hmmm... maybe some pectoral exercises are in order?). Ok... now keep that posture and place your hands on your chest as they were when you were laying down. One on your heart, one on your ribcage. BREATHE ... pay attention... remember how you were breathing when you were on the floor. Do not heave your chest up and down but instead expand and contract your ribcage sideways. Take some deep breaths.
Ok... now that you're all relaxed, try singing a little. Pick a note (got a pitch pipe or something?) take a nice deep breath (from your ribcage no heaving allowed) and try to hold that note out nice and steady. When you start to falter in pitch, it's time to stop and take another breath.
It's possible you're having a hard time staying in tune, or in pitch because you aren't breathing well. When your pitch starts to diminish are you noticing that you're about out of breath? I think your original post really did address this. Strength of voice, loss of pitch, and the fact that you're talking about breathing all tell me that this could be the problem. I know it's not really possible to SIT in this position and play guitar, BUT once you can remember how to "breathe properly" you'll have an easier time when you are seated. Of course... you are a "pro" with that strap and all so you COULD play standing up and sing!
Good luck! Hope this helps (and if not... please do video yourself doing this, because I always thought it would be amusing to watch someone ELSE doing these breathing exercises!! LOL)
.... disclaimer.... I am NOT a voice instructor and the information given here could be totally bogus, but it's how I was taught during private voice lessons... if it is bogus, I'd like my parents to receive a refund! I do have to say that even as a smoker of too many years, I have better breath control than quite a few people I know (my son regularly tries to have a "sing off" holding a note out until the other can't do it any longer... he refuses to take my advice on how to breathe) ... I attribute it to my lessons, course I could just have lucky lungs? I don't think I'm an awesome singer... but when I try, I can hold a note, and I probably sound much worse when drinking even if I think I sound better. In high school choir people either wanted to stand next to me because I would drown them out or they wanted to stand far away from me because I sang too loud and they couldn't hear themselves. I enjoy singing Italian Arias (opera) more than any other type of music.
I do really like GSE's advice tho too... that could come in pretty handy!! LOL!
edit: after writing all this I looked up info on breath control... all I could find is people telling you to expand and contract your belly... so, take it for what it is - maybe my teacher was wrong? The above works for me tho!
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What constitutes excellent music is in the ears of the listener.
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