Are you sure it is your rating that went down -11, or the rating of the problem?
tactics trainer
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Oh, yes, it was my rating that was -11. The average time was :17 and I took :36.
There appears to be a time element involved. If you take more than the allowed time (shown on the bar at the bottom of the screen), you lose points even if you correctly solve the problem. The allowed time for your problem was probably 34 seconds.
The purpose of your rating is to get the tactics trainer to provide you with problems that are at the right level for your training. I don't think you should move on to harder problems if it takes you twice as long as the average user to get the problem right. It would be best to continue to drill problems at that level or lower until you have them down cold.
With that in mind I don't see what the problem is with the rating change you got on that problem. Keep in mind it's a trainer, not a competition.
Maybe focus more on your accuracy percentage than your rating..?
What Loomis says above is very sensible; however, if one wanted to split hairs, there is a potential flaw in the way "average time" factors into the question of whether your correct solution affects your rating positively or negatively.
For me, it comes down to the question of what "average time" actually means. If it's simply the average time taken by every puzzler, regardless of the outcome, then this is really an argument for not paying too much attention to your rating. If 100 monkeys with twitchy fingers got to the mate-in-three problem before you did, and every one of them utterly failed it in five seconds or less, your rating is doing down through no fault of your own.
If it's actually the average time taken by players who got it 100% correct, well... now we're getting somewhere.
I'm positive the average time is only for users who got the problem right. As you point out, it doesn't make sense to include the average time of incorrect responses.
Hope you're right. (I'm not so much "positive" as "cautiously optimistic.") 
It's hard enough to move forward with your rating without losing points on problems you get right. I know you've heard this before, but I'm repeating it anyway. At the very least put a limit on how many you can lose. I just lost -11 on one I got right. I'm wicked frustrated, but that makes it worse.