The rain demos I've seen [2] [3] [4] are all in wet weather, but not this kind of heavy rain, where a promise of self-driving technology saving lives and property can be more assuredly realized. If anyone in the field knows of one of the contenders already working on training in such poor conditions, then please post a link to a demo if one is available.
[1] https://en.wikipedia.org/wiki/Clear_view_screen
[2] https://www.youtube.com/watch?v=xs9Gr9V2mOE
I'd be very content with an autonomous vehicle that would detect these conditions and pull to the side of the road to wait for things to improve before proceeding.
And if you're somewhere this is common (e.g. Florida), and there are still human drivers, you'll have to account for them not slowing down at all.
If you're in an area where flash flooding can happen, waiting may be a more dangerous option. Or you could be in a place where there is no place to stop.