Hi Sandi, it could be a number of things .. what exactly happens? Do they just shrivel up and die or do they kind of fold over on themselves and dry up? Are you seeing fuzzy patches on the seedlings stems? And are you using the same soil over and over?
It might be 'damping off' which is a fungal problem. Try a new batch with fresh soil and sprinkle some cinnamon, it's a natural anti-fungal on the top of the soil. You also want to keep the soil on the dry side of moist and use water that has been boiled and cooled. The chlorine level in your tap water may also be causing a problem. Set the heat mat to be on the cool side .. soil temperature in the low to mid 70's.