notification
most of my students who do poorly have always done poorly.

they fail (or D) subjects because they do not do/turn in work. parents aren't able to see these grades because there is no paper! i'm not going to the trouble of making an additional copy and writing on there that parents have to sign and then follow through to make sure it comes back--whew!
my students have planners (agendas) where i write in missing work, and all my parents know to look there for notes from me and homework assignments--they don't look; their problem.
i also send out progress reports--i used to send one out halfway through quarter. this year i sent 3 out during first quarter (i'm not sure how that happened, i meant to send out 2-before the 1st quarter report card.) i plan to send out at least 2 (probably end up being 3) every quarter from here on out. the first 2 had to be signed and returned (students received prize if returned within 2 days, no consequences the next 2 days, after that they owed recesses--this usually works pretty well). i only had one kid who didn't turn in progress report--couple days of recesses, i finally had him call dad to tell him that he had a progress report that he needed signed and would dad help him to remember to take care of it that night. i hate to be the bad guy--let the kids do it to themselves!
so, i'm saying, yes, your parents should be notified somehow that their children are failing (or even getting a D--some of my parents would be mortified with a C!) before that FINAL grade comes out--since there is nothing that can be done about the grade at that point. (on progress reports and report cards, i always "explain" the low grades: Franklin's math grade suffered from 2 missing assignments, 3 late papers, and 1 unfinished project. i have received almost 0 calls/emails/complaints since i started doing that--they don't have to ask me why, it's right there.
regarding your having parents sign tests: tests are only a part of a child's grade, right? so if students are doing well on tests but not doing well/not turning in assignments, a low grade
could be a shock to parents.