dont think you are doing anything wrong. make sure they are well watered with plenty of suppports for them to climb.

Sounds like a water problem if in the ground - or you're growing them in a shallow pot?

Do you mean the flower buds are drooping? If so,look up bud drop.....ideal conditions for it this year, because we have gone from a very warm spring to quite cold windy days at present. They will grow out of it.
As a matter of interest, how tall are your plants?
It's best not to let sweet peas flower until they are at least 2 foot tall. Early flower stems are usually weak and brittle and best removed.

Thanks for your replies. very much appreciated! The sweet peas are about 2 foot tall now and I'm growing them in pots. I feel hopeful now that later flower stems and flowers will grow stronger and that it's the inclement weather that could have caused this. I'm trying to give them loads of water as I was told they need it - hope this isn't contributing to the problem

If the pots are less than 18 inches deep, that may well be why you've got this trouble. Sweet peas of this variety need a good, deep root run, so a pot of 2 feet deep would be preferable.

Thanks bamboo! They are in big deep pots so fingers crossed ..........I feel much more hopeful now that as the season progresses so will my first first attempt at sweet peas !!

Good that they're in deep pots, no problem there then - if your sweet peas were here today, they'd be drooping from being battered senseless by the wind...