Why does my guitar drastically fluxuate out of tune every time I tweak or bend the strings?

Question

Is there away to make its ability to stay in tune less fragile...could it be the pegs or how taut the strings are around the pegs?

Answer 1

Getting the nasty things out of the way, it could be because it is a cheap guitar and the neck is bending, it could be there is a tension rod that is not tight.  

  At a less stressful level - look closely at the way the strings are wound on the pegs.  There should not be a large amount of string wound on, the string will dig into the thick layers and lose tune.   Loosen the strings and unwind the string, pulling the extra through the hole, so there are about 5-6 turns when the string is snug.  Eventually, you will trim the string hanging out.

  If you didn't have the problem or have solved it, and the strings still lose tune, make a small mark on the top of the peg (or side if your pegs run across) so you can see if the peg shifts position when you bend the string.   If it does, you will have to have someone who knows the mechanism to see what can be done.

  If the peg does not shift, go to the other end of the string and make a small mark on the string near the mount (forgot the technical name) and try bending the string.  You are looking to see if the mark moves - that means the string is pulling out of the anchor, which may mean it was not mounted properly - the mount depending on the kind of computer you have.