Phil Gollin - FDR/CVR search & recovery
I don't know about the status of the search, or about the 'true' battery life of the devices. Other people have commented on these issues. I used to work in the hydrographic survey industry, so I can comment on finding AF447 in the event that the pingers aren't detected.
A quick look on Google Earth at the seafloor in the region of the accident shows that it's pretty rugged. This means that finding the wreckage using the usual methods (sidescan sonar) might be tricky - boulders, cliffs, etc all give shadows which can look like wreckage, or the wreckage return can be hidden in those shadows. If you spent enough money doing surveys in all directions (so that the shadows are cast in different directions in each survey), and were scrupulous about investigating all potential contacts and databasing them ... eventually you would be 99% certain to find it. How long would it take & how much money? Could be 'a long time' and 'a lot'. I don't know the size of the search area, so I couldn't begin to estimate, but certainly tens of millions of dollars, and hundreds if it goes on for very long. You'd need deepwater ROVs to video each contact, and the day rates for the vessels which deploy those are very high (like $250k per day, IIRC).
If the wreckage is largely in one place, which may be the implication of the BEA report, it would seem sensible to continue searching. If it had fragmented in flight, chances of finding specific individual pieces (e.g. FDR, CVR) would be pretty poor. (I mean: you could spend $1bn and not find the CVR & FDR; so you would have to make a judgement up front as to whether it's worth doing the search, based on whether you think the debris field will be localized or scattered over tens of square miles).
I guess some people would have a view on whether it's in the interests of the French gov't to try very hard to find the wreckage. (I don't believe that sort of thing for a second, myself ... maybe I'm just naive).