Actually, a players PA never changes. Once a new game is started players with fixed PA retain this PA through the game and players with randomly generated PA (0 to -10) will have their PA assigned at the start of a new game and they then keep this PA throughout.
The clue is in the fact that PA stands for Potential Ability. CA (or Current Ability) is the only one that changes.
However, a players likelyhood of achieving their PA is affected by many things as discussed previously. It could even mean that they have no chance of reaching their PA, but it doesn't actually change their PA. It has been said, that for an older player, PA represents the best they were. If they never actually peaked at their PA, then PA represents the best they ever could have been.
In the same way, if a player has a very serious injury, or a long period of poor quality training, or isn't used enough, or for many other reasons, he may get to the point where he will never reach his PA. In this case PA still stays the same, it doesn't drop, but now just represents what he could have become, given better circumstances.
So, Raikan007, when you say "PA drops and rises as well due to several factors," this is not true. What may rise and fall is a players CA and also their ability to reach their PA, but not their PA itself. This is most definitely fixed throughout the game and anyone discovering differently will have uncovered a bug, or they will have used an in game editor.
A tip when looking at young players. Three attributes will have a large bearing on whether a young player will reach his PA and how quickly that he will do so. Determination, Ambition and Professionalism. Only determination can be seen as the other two are hidden attributes. There are two ways to determine these hidden attributes. First, you can cheat by using FM Genie Scout or FMRTE to look at the stats, or you can be honourable and play the game as it was meant and use the players description, your scout reports on these players and your own interactions with them, to determine how ambitious and professional they are for yourself.
Another tip. Don't get too hung up on PA. One player that I remember well from the past, Mehdi Mahdavikia, had a PA of 161 and yet was usually a world class winger, so CA/PA isn't everything and you need to look for players with the stats that you need.
Yet another tip. If you want to find potential wonderkids, but don't want to pay through the nose for players that have known high PA, you can do a very simple search on the games Data Editor. I don't believe that this is cheating, as the data editor is supplied with the game and is part of the package. I won't describe in detail, but essentially, you search "people" and then do a detailed search in which players PA is an option and then search for players with a PA no greater than -9 and no less than -9.
This will return you a list of all players in the game with a -9 potential, i.e. a PA anywhere from 150-180. You won't know in any particular game how good they will become, just somewhere in that range. No point in searching for players with -10 potential as this list is very short. I think that it's only one player, Aaron Ramsey. You must specify no greater than and no less than, or the data editor will return a much larger result as it will include players either below or above -9.
I hope that some of this is helpful.
