One thing I've started doing: I do not use knots at the top and bottom like that where the string splits and comes back together. As mentioned above if you put any pressure on the "split" I don't think it's as consistent. I go around the peep itself (fairly tight here though) and never have an issue once set.I do put a mark with a sharpie on my string just above and below the thread I use to tie on as a visual check that it hasn't moved, and it never does.
Wrap a cpl loops around the peep groove and string, cinch it, knot it, and burn the ends; done. Your peep won't move when you hunt, even "when crawling thru brush" as they like to say on the internet.