It is very dissapointing when new plants die. These things may be of help. Always water in very well for the first week(every morning give a long soaking). Also, it is a good idea to replant in the cool part of the day, ie.early morning or late afternoon. Do you have any fresh manure in your compost? That will certainly burn the plants so try to avoid until they are at least established. I also cover my seedlings for the first few days which seems to give them a helping hand.
Best of luck