I faced a very common problem in the game: lowering the reputation for no reason. Just yesterday, I played and increased my reputation (again) to level 4. This morning I go back to the game and see that the reputation is again at level 3. I get praise after almost every match, I don’t leave matches during the game, I behave decently. Can this be fixed somehow? It makes me very sad that my efforts are being wasted. 
The best thing you could do is to stop paying any attention to it: it’s a manipulative element of social engineering, and a rather unhealthy for certain psycho-types at that.
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Endorsement levels are BS. They mean nothing apart from a few free loot boxes every so often. They’re not a good judge of character and the system itself is so anal retentive that your endorsement level will decrease if you leave even a second too early. It’s best to just ignore the feature as a whole.
It’s also not accurate because when you lose games. Almost no one ever rates you. So 50% of your games mean nothing.
Focus on playing well instead. So many lvl 4 and 5’s are so bad because all they care about is their endorsement rating.
Like, what-the-frick-eva! You’re just salty 'cause I’m a 5 all day! But to the OP, really, pretend it doesn’t even exist because it really doesn’t mean anything. At most, be suspicious of high-level players with no endorsements at all but that’s about it.