I'm exploring a setting where Al-Qaeda manages to smuggle significant number of shoulder-launched surface-to-air missiles from Syria into Europe.
Would the airlines cease their flights until police locates the missiles?
RAND has released a detailed report on this after 9/11. They assume that airlines would shut down due to both the legal/financial penalties of losing 300+ passengers and the immediate drop in number of people willing to fly.
The short summary of action is that there are 35 instances of man portable missiles being used against civilian aircraft with 24 kills. Most of these aircraft were helicopters or other small propeller planes, so total casualties amounted to 500 people. Large 4-engined airliners are relatively safer, with only 2 of 5 missiles resulting in catastrophic loss of the aircraft. The latest report (as of publishing date) was DHL Airbus 300 struck by a missile while taking off from Baghdad that was able to turn around and land safely.
Fiduciary penalty to the airline would come to about \$1 billion between cost of the aircraft and legal claims from the survivor's families. US wide economic damage of a total flight shutdown is \$1.4 billion per day, to $70.7 billion per month.
It may depend on the airline and the policy of the government. Israel's EL Al apparently has various countermeasures both on the airliners and at Israeli airports.
Because the airline and air freight is such an important part of the global economy, you can expect that other airlines will follow the lead of El Al, and world governments will put heavy security around airport approach lines.
No, not in the long run. Expect some changes though.
This is assuming the threat can't be mitigated by somehow tracking down the missiles (e.g. it might be possible to simply buy a large fraction of them back by just offering enough money).
Shoulder launched SAM's are necessarily short ranged and the warhead is necessarily small. This means the only phases of flight a commercial airliner is vulnerable to them is shortly after launch / before landing. At cruising level they are simply out of reach.
So a way of protection would be altered flight corridors (emphasis on gaining altitude fast, lower altitude as late as possible before landing). Closely monitored/prohibited zones around airports could be established to protect airliners during takeoff/landing. In case where this isn't feasible (urban airports), checkpoint systems could monitor entry into the zones (expect something like border control when entering a city near an airport).
By extension this is exactly the same what we already do to protect airplanes against bomb threats and hijacking. Just the scale is much, much larger.
There is also the possibility of active countermeasures, flares (either from the plane or ground based), monitoring by drones, ground based interception systems (all these exist to an extent for military purposes already, although adapting them for the job and deploying them in numbers will take time and money).
In consequence flying would become more expensive (to pay for all the security), and for vacation trips car/train/ships probably see more use, leading to a decline in passenger counts (some airlines will go out of buisness). The number of airports in operation would probably be drastically reduced by this, either due to them no longer being commercially viable or their location being untenable. Regional flights may become commercially incompetetive with other transportation.
Intercontinental flights on the other hand will probably continue and passenger counts would be impacted less than regional, there is no alternative available that can compete in speed. Even if ticket prices went up 10 or 20 fold, there would still be customers willing to fly.
In this litigious, risk-averse world, I'd have to say the answer is yes. A single jumbo jet full of passengers would produce losses of billions of dollars for the airline using it, since the threat would be known and the airline arguably conducting its business "with a reckless lack of concern for the welfare of its passengers". Or at least, that's what the plaintiff lawyers would say.
Except for El Al, where they have installed flare dispensers to defeat heat-seekers.
MANPADS are not likely to be present in the US, though. They are tightly controlled.
Also, they require specialized batteries so can only last so long without new ones. So they have a limited shelf-life. It's not like you can replace D batteries to make them work.