I moved my adgroups into new campaigns, same ads and keywords, to better organize my campaigns. Now I'm getting "rarely shown due to low QS" is this because I previously had better keyword history? Should I give it some time to regain it's score?
Also, I have 6 different product lines, I used to have them all in the same campaign. I moved each line into its own campaign so I could organize their adgroups better.. Is this a good way to do it?
I don't know if it's because of keyword history, although I'm sure some here will say that's the reason. Give it some time, it might regain its score. But showing that message just for moving things is not a good sign.
Having one campaign for different lines is a good way, and usually done that way.
You'll generally have to wait to receive some impressions and clicks to see your QS return. A big part of your QS is your CTR, so once you start getting similar results (or better) than before you should start to see a steady climb. Google has stated before that once you receive around 2000 impressions, you can assume that your QS at that time should be quite steady.