My old, cheap acoustic keeps going out of tune real quickly, so would changing the strings prevent this? The strings on now are over six months old, because I got a new acoustic. It normally stays in tune for a long while.
Try a little nut sauce. Then there are some strings that stay in tune for acoustic but then again if you play everyday I would change them more than once every 6 months. Check your tuners, check you saddle bridge make sure you pins are set tight, finger tight. try mixing graphite from a pencil and Vaseline and a-ply to the nut. In the string slot.
6 months old isn't bad at all. I'm guessing it goes out of tune because it's "old, cheap acoustic"
changing strings can definitely help your guitar stay in tune.