Tongue Blocking draw
I am having draw problems while tongue blocking, may be for the same reason. When I try to play something fast (not so fast) the draw note collapses.
For me is easier to draw on higher notes than the lower ones.
It could be that your lip and tongue are collapsing, causing the reed to choke/bend. More likely though your tongue is at fault... this is the cause in most cases. Drop the tongue down in your mouth... most likely the middle is humped up. Go to a mirror... close your eyes... open your mouth... drop your tongue to the floor of your mouth... confirm it feels right... look in the mirror... most likely your tongue is humped up... work on this. Also, using an "E" position (back of the tongue touches the upper-back set of teeth) can also be effective.
I had the same problem with draws when tongue blocking. I started learning with the "pucker" (shudder) method and began tongue blocking anew here. After a while of practicing, the blows and draws now sound equally well without much thought put into it. It took me a solid couple of weeks of practice to get it down though. Just keep working at it and don't give up.
Smile... that will help keep your lips from "sucking" in. Also, make sure you're not pushing your tongue on the harmonica... place it softly on the harmonica. Good luck!