I know of a case where a small GA aircraft has had three owners since it was manufactured. However the only airframe, power plant and propeller logbooks available for the airplane are from the most recent owner and no other logbooks are available from the two owners prior to the current owner. The current owner's logs are good with the required annuals, engine overhauls, etc. documented and incorporates all FAA and manufacturer ADs to date. Does this decrease the value of the aircraft? My first thoughts are that yes, it will, as I have no idea as to what happened to the aircraft prior to the date the current owner obtained it, but I'm not totally sure.
It does decrease the value but may also be a good deal for a buyer going in for a long term purchase or a flight school leaseback machine. I would not be opposed to buying a common GA plane with missing logs provided the plane "checked out" during the prebuy. I'd pay nothing near VRef value, however.
Humid climate history, as much as could be determined, may be a non-starter. Usage of <50hrs/yr over last 3-5 yrs would likely be a non-starter. Obvious or poorly repaired damage is a guaranteed no-go. An in-flight speed check would be mandatory as would an oil analysis on well-used oil (>10hrs). Little rubber parts like gaskets and hoses can be good "attention to deal" indicators. If the owner took care of little details the big stuff is probably fine too (still, verify everything!).
Nothing wrong with missing logs as long as the price is right and a good inspection is performed.
What is the subject aircraft?
The value impact will depend a great deal on how far back the logs go. If they only go back a few years on a ~40 year old plane then maybe a ~50% cut is in the ballpark. If they go back 10yrs on the same plane then maybe ~30%. Personally, I'd make a absurdly low offer. The owner knows (or will very quickly learn) that he's playing to a tiny, tiny segment of the buying market. Your borderline insulting cash offer may net you a servicable plane that will give you years of faithful service.
In my experience, a common GA plane with no verifiable damage history, unremarkable avionics, and decent (not "great") P&I will sell for the VRef price minus 10%, give or take a few bucks.
As they say, there is only one reason a plane won't sell: price is wrong.
As far as piecing together the history goes, check the NTSB database and google the N number. People love taking pictures of damaged planes! The 337 CD from the feds is a given...gotta do that. Use the 337s to track down the shops. If they're still in business give them a call and see if thay have any additional records or information on the plane. They probably won't but it's worth a shot. The 337s are also an indication of where the plane may have spent time. A bunch of 337s from AZ would give me warm-and-fuzzies. Not so much with a bunch of south FL records.
It will most definitely decrease the value of the airplane. How much is not easily answered. If the current owner has owned the plane for a long time and all the ADs are complied with then probably not much of a decrease in value. If they have replaced the engine and prop—even better. However, if the current owner has had it for a short while, then maybe he’s selling it for a reason related to the missing logs.
Maybe there was a prop strike or gear-up with a previous owner and they didn’t do the repairs properly. Or maybe there is a lien on the plane from when the last owner didn’t pay the shop. Or it could be that the plane was perfectly maintained but an ex-spouse kept the books in a nasty divorce. That’s why it is difficult to say how much the missing books decrease the value.
You can get the records for the airplane from the FAA in Oklahoma City to see if there was major damage properly repaired. The A&P is supposed to file 337s for major repairs and modifications.
In any case, you’ll need to have an A&P who is familiar with the type do a careful pre-buy.
Whether you should buy a plane with missing logs partly depends on how long you intend to keep it. Just like you are concerned about missing logs, the next owner will be too. If you plan to keep it for a long time, then you probably shouldn’t be too concerned about the difficulty of selling it later. If it’s a transition airplane for you, then know that it will be more difficult to sell.