NOTE: Many speculations have been proved wrong and new ones have been discovered. OP will no longer be updated, follow the discussion.
I saw there's one post about this topic already, but last replies are from 2013 and the info is either inaccurate or insuccifient, so I decided I might as well go ahead and elaborate in the working of Skillquant more from my point of view, having plenty of material to support facts and speculation with.
So, you might ask "why did my SQ rise/drop this much?" Well, there's many things that affect your SQ in the background, and I'll cover some stuff I've acknowledged.
First off, most importantly, SQ does not represent your speed. Rather, it represents your activity and versatility. These being said, it's obvious that there are some people with high SQ that cannot be near the top in the leaderboards, however, just in case I won't name any example(s) here. Sure, one could say it's because they haven't played the game for a while. Now, while this could make sense, the commitment and activity comes in. Your SQ will most likely drop if you are inactive for long periods of time. The more you play, the more chances you will have to either keep your SQ as it is or rise it. However, activity is not the only way to keep or rise your SQ. Hold on, I mentioned keeping and rising only. So, let's cover the SQ-lowering actions next.
While I don't have a lot of experience on things that affect on your SQ negatively, I'll try to point out some important things. Firstly, myself being over 1,000 SQ, I don't do a lot of mistakes. Mistakes are however a thing we all do. That being said, it should not affect on your SQ. Penalties are another thing. Quick race/hotlap penalties, as I've seen it, won't affect on your SQ. Crashing won't either. However, one thing that CAN lower your SQ, is, in this case, lack of pace. In quick races, however, bad races can lower your SQ. I'm not certain what affects your SQ in these but most likely the finishing position. Quick races are also an effective way of gaining SQ so it's pretty much do or die.
Now that I'm writing this post on the 19th of July, I woke up this morning to see my SQ had gone from 1,056 to 1,055 suddenly without me taking action. This was most likely achieved by the fact that I got overtaken in a hotlap event. So, in a sense, the lower you are on the tables, the more your SQ might drop. If I were to improve more on that event (and not just gain my position back) the SQ should be restored. However, I got 1,056 again simply by test driving a new car I haven't tried yet, in a quick race. Trying more cars (and tracks) is a major factor in the calculation of your SQ. Like mentioned above, versatility is the other counterpart of your SQ. This is what it means. You shouldn't stick to just one or a couple of more cars, in which case you might be stuck on your current SQ for a while before it will rise again, OR even lose SQ. Rather, you should try as many cars and tracks as possible. From my point of view, since I no longer possess a low SQ, gain 1 SQ point per new car I try out sufficiently enough. However, since I only own 52 cars at the moment and have tried less than 100 in total, this wouldn't mean I could go over the 1100 SQ limit. It's obvious that the higher you go, the tougher it is to improve, such like gaining experience points towards the next level in RPGs. Works the same way. So later on, I assume this would mean I would need to try 2 cars instead for 1 SQ point.
That's all there is to it, really. I repeat, SQ represents your activity and versatility. The more actively you try more and more cars and tracks, the higher your SQ will be. However, like many people have noticed, some people can be very quick though their SQ is low. This can either mean they have just started and already have lots of experience from outside SRW, or simply don't have a higher SQ yet as there might be a delay in gathering the data, OR they have sandbagged. Sandbagging means relegating to lower ranks in order to achieve good results easier. A thing I find weak, honestly. If you want to progress on your career, keep pushing. You won't get any profit by relegating and dominating the field. It is quite obvious when they look at it. So, I encourage everyone to try out many combinations if you wish to increase your SQ!
Please share your own experiences below if you have anything in mind and leave your thoughts below if found this helpful.
P.S. Try also as high-classed cars as possible. My SQ went down from 1,055 to around 1,020 after trying a kart event. It's fair to say a free, slow car affected in my SQ, no matter how good I was at it.
P.P.S. Practice mode won't affect on your SQ. Online activity only.