Leaking on 2nd day of period

Hello all,

I am 42 years old, never had kids and been using the Diva cup small every month for the past 2 years. Everything is great except for the second day of my cycle due to leaking. No matter what I do, I get leaking ONLY and ALWAYS on the second day. My period does seem to be heaviest on day 2, however, I have noticed that the cup will leak even if it's not full, or even empty. Sometimes I will put the cup and immediately start bleeding into my pants. This is driving me crazy. Any ideas what could be causing this? Should I switch to a different cup and if so, which one? 

Many thanks for your comments !