Reeds go out of tune for several reasons. Here are just a few:
1. Metal fatigue. The reed is essentially a piece of spring-steel (not very dissimilar to what factories used to put in a support bra. While you play the reed has to flex back and forth hundreds of times per second. It is pretty strong but at some point it may start losing a bit of that spring and go out of tune, and eventually even break.
2. Valves: Especially leather valves become stiffer over time. Booster springs may lose a bit of their strength too (certainly plastic boosters which are rubbish). When a valve changes the resistance it offers to the air flow also changes. If the valve becomes stronger (because stiffer) the frequency drops. If it becomes weaker, or if the glue that holds it on the reed plate becomes weaker, the frequency goes up.
3. Wax may dry out. When wax ages it loses its "glue" property. The reed plate may no longer be held firmly attached to the reed block. When the reed plate is loose it can vibrate by itself, and the reed not only goes out of tune but also gives a weaker sound and perhaps rattling too.
4. Some accordions do not use wax but have nailed reed plates. The nails may lose their grip over time, causing loose reed plates just like with hardening wax.
5. When the rivet no longer holds the reed tongue in place you get similar results as with the dried out wax or loose nails. You can take out the reed plate and hammer down the rivets.
6. Air leaks change the way the air flows and that influences the tuning. Bellow gasket tape may start to leak. A reed block may warp slightly so some spots do not seal well on the sound board, and that air leak will produce a note that's out of tune and has a hissing sound as well.
7. Valves may fall off. That gives a very sudden change in frequency. What was dry tuned suddenly gets a strong tremolo. Reeds do not go out of tune suddenly. If you suddenly get a large pitch shift in one direction it is almost always a valve that has fallen off. (If not, then it's a reed that's about to break.)
8. Rust. When a reed rusts it can go sharp or flat depending on where the rust is. There are many ways to clean rusted reeds, and they all work but they also all fail to solve the problems permanently. Rusted reeds simply need to be replaced. Rust is most often developing under the valves first (so on the "blue" side of the reed tongue). When the reeds as you see them on the reed block look fine it's no guarantee they are not rusted under the valves.
I'm sure our expert JimD can still add more causes to this list.