The trick to Rudbeckia is stiffness of the stem right where it meets the flower - it must be stiff and not at all soft or floppy. This will only occur on flowers that are mature.

To get the hang of this, put your thumb and forefinger on either side of the stem just below the flower head and by moving your thumb toward your finger, check how stiff the stem is. There should not be any 'give' or bending. Try this on mature flowers, old flowers (past their prime), and those just opening and you'll soon figure out the difference. When picked at the right time, and set in floral preservative (or a recipe), Rudbeckia will last at least 10 days or more.

Pudge:
Thanks sooooooooo much! They last so long in the garden, I knew I had to be doing something wrong. Tomorrow, first thing, I'll be out "feeling" stems of rubeckia. Hopefully, they won't all be past their prime.
Again, I've learned so much. Gardeners must be natural teachers!