Are you hardening them off when you put them outside? Any seedling that you bring outdoors should be exposed to the elements gradually. You set it out in the shade for only a few hours each day, gradually leaving it out longer over the course of a week or so. If you put it right out in the hot sun and other elements right away, it will kill it.
Another thing you could try would be to plant the seeds and cover the area with a row cover, which is a light fabric that lets water and fabric in. One of the most popular brand names is Reemay. You might be able to find it at a garden supply store, or you can order it online.
Good luck! I hope it works out for you.
