The plant started to be very wilted then after a couple days, total drying out.
Potato Plants Dying One After Another
Certified GKH Gardening Expert
To much rain and poorly draining soil can cause root rot and or the plants can become affected with fungus and disease.
Waiting and watching is the advice I can pass on!
If they are just wilting and the days are dry moving forward, they may be able to recover.
Here are a few links.