There are lots of posts on this forum with this problem. Some describe it really well.
1. No peep tie in untill U shoot at least 200 shots. Tie in the peep and start shooting. Then re-align the peep.
2. Your string has to be in good condition, eg. If the end points are served with twisted eye on it, your screwed no matter what.
3. I try to avoid rotation correction using d loop. This depends how you pull string during shooting, wide rounds pulls will rotate d loop/peep. I'm using soft d loop material to help with that as well.
4. D loop tie in has to be opposite sides or it will pull to one side
5. I use draw board to check peep alignment
6. I started to use peep adjustment (small plastic in string above peep), but I'm not satisfied with that.
7. Even small peep misalignment per shot basis will shift the arrow on horizontal plane. It is vital to keep it straight as close as possible(target shooting 10s vs Xs).
Mind you, I customised my sight housing to fit my peep size precisely.
I write all of this as I threw away new aftermarket string recently. My peep rotation was ~20deg on shot basis. This threw my score down the drain, and heaps of fustration.