What type of rain are ya talking about? Torrents and thunderstorms, or ANY rain? I don't think the rain flattening the plant will kill it, but I guess it's possible, if the leaves get buried by soil washing around. Lettuce will do that, but this is the wrong forum. We've had a lot of rain lately, and my D. Filiformis' got dirt on their leaves,(Same w/ the Sarrs) but didn't die or shrivel, though the Proboscidea's in the garden have a permanent bend in them from the wind. The other option is the depth. I grew Filiformises in shallow (4") undrained containers, and they were dying left & right. Now they're in a 12+ inch depth bog with a drian hole, and none died in the past 3 months they were in it! From what I understand, they like drier conditions, so your problem might not be so much the rain, as the additional H2O the plants are getting from the rain and the flooding in the bog which results in root rot.
As for the D. Binatas, they grow around the same areas as the tuberous and pygmy sundews.(I'm pretty sure on that, correct me if I'm wrong) Those areas get a drier summer, and one form of Binata goes dormant at the same time as the pygmys and tuberous dews (Dichotoma small red form or something like that, you know, the weedy one?) They may also like a drier or more drained soil. Mine are outside in a 4" pot with a 1" scaucer, so that hypothesis may be wrong. For those I'm leaning more towards the leaves being covered in dirt and the shock of being flattened.Good luck!
One thing, HOW DO YOU GROW D. CAPENSIS' OUTDOORS! I've tried to, and I (un)successfully have 4 poor little things being mistreated in the 90 degree weather we've been having. I could bring them inside, but I like killing bomb-proof plants.... I'll bring 'em inside someday.