I have had this same issue for the past few weeks now (no notifications in the status bar, no sounds). I have missed out on some opportunities (work related, slick deals etc) due to this bug by not getting notified promptly, it has definitely been a annoying bug.
I have tried everything as far re-installing yahoo mail app, trying other apps such as K-9, changing all different kinds of settings within android and within the yahoo app.
However, I got the notifications to work today! (knock on wood)
I went to:
Options >> General Settings >> About Mail >> Report a Problem
and I reported the issue through the app, saying something along the lines of "I am not getting notifications in the status bar on my Android device. It used to work just fine"
Within 30 minutes of me sending that report, my notifications started working again! It could be a coincidence. Or perhaps Yahoo did something on the backend. I am not sure, but it is defintely worth a try for those of you still having trouble.
BTW, I do use Gmail and it is great, but I just prefer to use both. Dammit I use too much Googles! (Search, Gmail, Chrome, Android, Voice, Plus, Maps, Docs etc)