The missing jet had requested a "deviation" from the flight path due to bad weather, AirAsia said.

Indonesia's transport ministry said the pilot had asked permission to climb to 38,000 ft (11,000m) to avoid thick cloud.

I don't believe that survival at sea after an airplane going down is too common. I can't even remember a time when anyone was found alive after a civilian airplane disappeared from all contact.

Exactly- survival at sea. That's a different thing. Chances of both survival and rescue are worse.

It's rare, but there have been survivors when all contact is lost.... here are a couple off the top of my head.

1997: Korean Air 801 at Guam.... a perfectly good aircraft (Boeing 747) flew into a hill while on approach to landing. aka CFIT (controlled flight into terrain). Surprisingly 26 survivors of 254 crew and pax

1995: American Airlines 965 at Cali, Colombia... much went wrong with this accident. B757 flown into a mountain. 4 survivors (initially 5) of 163 crew and pax.

1993: Asiana Airlines 733 at Mokpo, Korea... another CFIT accident. 48 survivors of 116 total crew and pax.

One thing these types of accidents have in common is they were on approach to landing. Flying relatively slow and low- ish. The impact is "less" severe (well, any impact in a commercial aircraft is severe) as opposed to something breaking up at altitude (30+ thousand feet) and at high speed.

One notable accident... Japan Airlines 123 in 1985. A Boeing 747 lost its entire vertical stabilizer. The pilots were able to wrestle it down and somewhat control the crash. 4 survivors out of 524 crew and pax. It was amazing the crew was able to control the aircraft for 30+ minutes as no subsequent flight crews were able to replicate it in simulators. I think the longest replicated time was 10 minutes.