I feel for you as I had the same problem.
Don't know if it was collagen or rolling veins, but many times a draw wasn't successful. I think it is somehow the body's defense mechanism to harm. This happens on death row on a regular basis. Operator error and stress compound it, too.
So, here's the solution I finally used....
.....Have them draw blood using a butterfly
from your hand
It has never failed with me. In fact, I've taken many Orencia 45 minutes infusions from my hand vein.
After you get used to it (a little more painful, but not much), lose the butterfly for a regular needle and you'll cut the draw time in half.
Let us know if this technique works for you.
Best wishes and best of luck!