The tuning pegs might become stuck to the side of the pegboard holes they are in. Also, if the strings are not kept at the correct tension, there is a real possibility of the iron frame becoming warped or even breaking.

Same thing happens with a guitar if you leave it without strings or heavily detuned. The neck can begin to warp and become very easy to break.

That's also why you have a truss rod, to prevent/correct neck warping. I've never seen a neck that was easy to break though...

To add to the discussion... the location of a piano has a large impact on its ability to maintain its tune. For example, humidity plays a major role with impacting the soundboard, as well as all of the various wooden components of the piano. In general, a piano should be located in a consistently-maintained environment with regard to humidity and temperature, away from windows and direct sources of cold and heat (e.g., HVAC registers).

It usually doesn't. If the strings or pegs are worn out, those may need to be replaced, but from what I understand that's a fairly infrequent occurrence.

The strings are under a lot of tension, and if they're way out of tune simply cranking them a semitone back into tune won't do much. They won't stay put.

From the bit I've dealt with a piano tuner, they told that you're generally not supposed to tune it more than I believe it was about 4 cents each time (a semitone is 100 cents). It gives the strings and everything else a chance to adjust before tuning again. It's a similar idea to a guitar I think... If you just crank the tuning pegs around a few times it generally doesn't stay in tune very well. It needs to be a slow process.

If you've got an old, very out of tune piano it may take several tunings over a couple of years to bring it back into tune, but it should be do-able.

There's also humidity to take into account - you need to keep the humidity pretty constant while you do this or the wood will absorb/release water and change shape and bring the piano back out of tune.

It doesn't lose the ability to be tuned--the state of the piano merely drifts over time if it is not maintained--imagine your teeth drifting in your gums without a retainer, for example. If it spends 80 years warping a certain way, it will just take another 80 years of careful tuning to warp it back in a gentle, safe way. Most objects are not lucky enough to get 80 years of human attention after 80 years of inattention (stradivarius violins are a notable exception--these violins stay in tune just fine, despite being over 300 years old--they are nice enough that people have decided to keep tuning them).