So is the plasma burn-in from constant picture still a problem, or they recover after a while (just a temporary memory)?
Excellent question, I shall use this opportunity to educate some folks (hopefully), and dispel some plasma myths.
Fact: Plasmas CAN suffer from some IR (image retention). This can be witnessed when leaving up any static content on-screen for a moderately long duration (few hours will do). Think TV station logos, or static heads-up displays in games. Since these common causes of IR are generally very localized (small areas of an overall large screen), they may or may not even be visible during viewing of other content.
The key is that this is NOT permanent, it disappears fairly quickly, when viewing other content.
Fact: IR is NOT BURN-IN. Burn-in is a completely different phenomenon, although it:
a) is triggered by the same behaviour (only much more extreme)
b) LOOKS exactly the same
Both of those are reasons why the myth of burn-in is so prevalent. Burn-in is (fairly) permanent because it is uneven wearing/aging of the phosphors (which comprise each pixel). This is bad, but it is also next to impossible to experience in a typical home viewing setup as this would require hundreds of hours of wear repeatedly on the same pixels (think airport depart/arrival screens).
IR on the other hand is caused by residual charge in the pixel (technically the plasma cells that comprise the pixel) which changes the luminance characteristics of the affected cells (and thus pixels). This goes away over a period of time depending on what those pixels are asked to display next.
The important thing to remember is that IR is NOT cumulative, so once the residual charge is discharged, it is gone. It has no impact or grounds in the wear of phosphors (which is what causes the permanent burn-in).
peace.