The last couple of cycles, my period has been so incredibly heavy that I have to constantly empty my diva cup and it leaks quite a bit too. It fuckingsucks. I have an IUD and just started having regular periods recently (I'm still nursing my 14 month old). I had no issues with my diva between my two pregnancies (also with IUD).
I switched to heavy tampons for now, hopefully it works ok.
(and yes, I have the size 2 diva. I wish they made a size 3. omg, that is so wrong and pathetic, lol)