Tuning stability describes the amount of time a piano can stay sounding in tune after it is tuned.
The three factors that affect tuning stability are: condition (usually age-related), location & environment, and playing.
Pianos are tuned by turning the tuning pins with a special wrench-like tool called a tuning lever or tuning hammer. The number of tuning pins in a piano averages around 230 or so and they all get turned during a normal tuning.
Each tuning pin is mounted in a block of wood called, cryptically enough, the pinblock.
Tuning pins in a grand piano -- cross-section side-view
During manufacture, the hole drilled in the pinblock is a little bit smaller than the diameter of its tuning pin so that it sits very tight. It needs to be tight to resist turning because the string tension wants to make the pin turn. Over time, wood loses moisture content and shrinks -- the same way a sponge does when it dries out. When the pinblock shrinks, the hole gets larger and the tuning pin is not as able to resist the string tension. Eventually, it can't resist at all and unwinds as soon as the tuning hammer is removed. A dry environment speeds this process. This condition is rarely present in pianos that are under 50 years old.
Once the pinblock is shot, there are a few different ways to address it:
First consider the age of the piano. It also helps to know when the last time the piano was tuned. If it was tuned a couple of years ago and sounds really bad, pinblock problems may be present. Musically speaking we can observe the following in troubled pianos: octaves that sound like major 7ths, a single notes that sound like a two notes a half-step apart, or a loss of a consistent chromatic scale when going up or down the keyboard. If the piano hasn't been tuned in a long time (like, decades), a tuning will need to be done in order to see how well it holds. (Although if a piano hasn't been tuned in a long time, there a likely other problems present from neglect.)
LOCATION & ENVIRONMENT
An unstable environment can also affect tuning stability. When a piano is moved from one house to another, it is usually recommended to allow it to adjust to its new environment for 10-14 days before tuning it. This allows the piano to settle into a different temperature and humidity. Schools and churches which have heating and
cooling cycles that can vary up to 10 or 15 degrees will keep the piano in an ever-changing state of temperature and humidity, thereby lowering the tuning stability -- and requiring more frequent tuning. A similar situation exists in homes where the piano is near an often-used door -- the environment around the piano never stabilizes and so the tuning stability is affected. Location of the piano should be carefully considered.
Playing the piano, believe it or not, has the least effect on tuning stability. On older pianos the effect is greater due to a compromised pinblock as described above. Sometimes the impact and vibrations of playing are enough to affect pins that are not so tight to begin with.