Did you harden them off before you put them outside??

Harden off = slowly acclimating them to the outside elements

Why not try to grow them outside in a container of some sort.

What kind have you tried in the past.

Also, what goes wrong outside... do animals eat them? do they just fall over in the sun? disease?

That will help narrow down some things

Keriann~

I've read that sunflowers don't like to be transplanted. However, the slugs will mow my sunflower seedlings over in one night if I try to start them direct. So I start them in those jiffy pots--the ones you can plant directly in the soil. That way, I'm giving the seedlings a start before setting them out as slug food, but I'm not disturbing the roots when I try to move them.

Here is a link that might be useful: my blog

Here are some good tips for growing sunflowers from my personal knowlege and from some research:

Try planting them 1-3.5in into the soil if you are using a large container or not using a container at all, however if you are planting them in a small container then I reccomend 1-2cm deep.
Do a soil pH test, the ideal pH for sunflowers is 5.0-7.0, to raise the pH of the soil, use wood ash to lower it use coffee grounds. Here is a link with a chart for plants and recommended pH levels: http://www.eutechinst.com/tips/ph/15_soil_ph.pdf
Good Luck!
~Lindsey:)

Here is a link that might be useful: http://www.hort.purdue.edu/newcrop/afcm/sunflower.html