Hi there Cara,
Your poor duck, that is awful that you had to put her down
I too have had a duck with a prolapse this year. I'm not 100% sure what caused it, but we do have too many drakes. The duck with the prolapse was born in September though, and she started laying in mid February, so I wondered too if she might have been quite young to start laying, and that would have caused it. She has also laid some quite big eggs. She is a white campbell duck and besides her mate, the rest are all Shetland Ducks - quite a bit bigger, so maybe the drakes have been too much for her.
I got the vet to stitch up her prolapse. This seemed to work fine, until she started laying again, and her poor bottom came out. She's gone into moult now,and the drakes don't seem as bad as they were, and I think her bottom has maybe healed itself, as it looks its functioning more normally now, and doesn't seem to be sticking out.
Maybe you could keep your drake locked away from the ducks for a while, until his hormones dampen down? Maybe this would make him worse though! Maybe if you don't want any baby ducks you could ask the vet to do something?! Don't know if vets are in the business of sorting drakes though
Would be interested to hear how you get on with him.