Ps3 – If I buy a game from PSN on ps3 Is it permanently mine

I've found a lot of posts from people who are asking the same question as you: some examples are below.

• Outrun removed from US store - supposedly due to a licensing issue with a car in the game
• Joust and Championship Sprint removed from US store - supposedly due to licensing issues with the company that bought Midway (Midway titles were supposedly removed from the XBLA store as well)
• Bishi Bashi Special removed from EU store - no reason known
• Mortal Kombat 2 removed from US store - removed due to issues after a firmware update, was supposedly restored afterward

However, I don't see anything from Sony, even though they blog about games being released and people comment on the blog about other games being removed.

Despite that, I would answer your question yes, Sony does remove games from the store. Why?

• Legal reasons: they used to have rights to the game and don't now, or some content in the game is illegal in a region
• Technical reasons: something is found after release of the game or of a firmware update that causes significant problems for gamers
• Sales: perhaps someone can find a specific reason for this in the PSN store; maybe it's similar to the XBLA store, where low-selling games have been pulled to "make room" for more popular games

At least in one case, games reappeared in the PSN store after they were removed. Maybe Vagrant Story will eventually reappear too.

If you play games without signing up to PSN then you will not be able to download any patches or updates for the games. This would mean missing out on additional features added after the game was released, and of course any bug fixes. How important this is depends on the game, as some games get a lot more post-release support than others.