Unless the strings or the tuning pins are damaged and need replacing, a piano can always be tuned perfectly.
But the real question is: how well and how long will that piano hold the tuning?
A good quality piano which is tuned regularly becomes "well conditioned" and will hold the tuning well and for a long time.
On the other hand, even a good piano, if neglected, will lose its conditioning, and may not hold the tuning for very long.
In such a case -- i.e. after a piano has not been tuned for a long time -- it will have to be tuned a first time, then probably tuned again after a few days or a few weeks, and possibly one more time not very long afterwards, in order for it to settle back properly.
Afterwards, and as a rule of thumb, a home piano should ideally be tuned every 6 months or so to remain well conditioned and hold the tuning properly.
Concert and recording studio pianos, of course, are tuned or checked before every important event, but that's another thing...
(Source: conversations with a friend who is a professional piano tuner and technician. I also used to tune friends' neglected, dust-collecting pianos as a hobby.)