If you find yourself having to retune your guitar after every song you play on it this one is for you. I used to have severe tuning stability problems with several different instruments over the years, all of them from well known, highly regarded brands and professional grade.
When the problems started on my G&L Legacy HB, I was so sure that the tuning machines are responsible, that I got a six-pack of matching G&L locking tuners, thinking that these are going to end my misery once and for all! Not only they did not solve my problems, they didn't even make a tiny improvement, well, at least not in the tuning stability department... I love locking tuners for the ease and speed of string replacement, but other than that, they are just regular tuners..
The Physics
Ok, lets break one myth: tuners of reasonable quality don't rotate in any direction because of string tension on lack of tension, for example when you release a bend or depress a whammy bar. They just don't. So, how come your strings go damn sharp after those tricks?! That was a mystery to me until the tuners replacement failure forced my limited brain to think that something must be holding the strings strong enough, keeping it from returning to it's original position after I release the trem arm, which tightens the string and makes it go sharp... and that thing can be one of two, the nut or the bridge. These are the two friction points with the strings and friction can definitely cause this!
So, since my bridge and strings were shiny new, I didn't have any reason to think the problem was there, so I turned my attention to the nut.
Going Nuts..
The nut serves two functions. The most obvious one is "fret zero" right. It defines the beginning of the guitar scale and if it wasn't there, the pitch of open strings would be defined by the length that's between the tuners and the bridge, which wouldn't be very convenient for guitar builders and players alike... just a thought..
The other function of the nut is tone. Some materials sound different than others, some sustain differently and may have different characteristics that may or may not increase friction.
The most basic thing to look at when trying to fix tuning problems caused by a bad nut (most tuning issues are related to the nut) is the size of the string slots, especially if you increase your strings gauges! If the nut slots are too tight, you surely have unwanted friction and sooner or later that's going to translate to tuning problems. If this is the case, I would recommend taking the guitar to a serious guitar dude! This kind of job requires some tools that most households don't have and of course skill experience that you may or may not have. Just to be clear, going about it the wrong way can ruin your nut at best..
If your string slots fit the strings well, they might just be a little dirty or dry. In this case, it's really simple! Remove the strings and clean the nut slots gently with a toothbrush or toothpick, or something that can get in the smallest slots without damaging the material. Then apply some lubrication to the slots - a little goes a long way. You can use silicone oil or consult with a guitar tech or maybe google. Clean any excess and re-string the guitar. Do all the regular stretching, tune up and you're good to go.
There are many products on the market specifically for nut lubrication, which I'm pretty sure they are just silicone oil, or another material with a different label on it.. Anyway, find your lube and make sure it's on that nut!
Happy bending!