This probably sounds like a dumb question, but what are the things called that you put on your guitar that lock the strings so they stay in tune longer?
You can't just put a locking nut on any guitar - it's a totally different mechanism than a regular nut. Your headstock/nut slot has to be cut for it. And it just honestly wouldn't work that well for a non-locking tremolo.

What you could do is get locking tuners though. Those supposedly help a bit when you don't have a locking trem.
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Get a graphite (graph tec or tusq) nut and locking tuners. If it still falls out of tune, you're doing something wrong.

Though most of the time when people complain about tuning problems, it's because they're doing something wrong. Whether it's winding the strings on the peg wrong, not lubricating the nut, not stretching the strings, upping string gauge without checking to make sure the nut slots are still big enough.... I could go on all day.
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Stretch the strings out. Makes a world of difference in tuning stability.
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