If I set my wipers to 'auto' and the sensor detects enough water to require the highest wiper speed, the wipers just stop wherever they are on the screen. Similarly, if I select maximum speed, the wipers stop.
Any idea if this might simply be a relay?

I had the wipers randomly stopping on the screen like you have. With me it got progressively worse and made the car unsafe to drive in the rain. It needed a new wiper motor which, luckily for me, was done under warranty. FL2 HSE Auto Galway Green
Evoque SD4 Auto Blue.
FL1 HSE TD4 Manual Black - Gone.
RR Classic V8 EFI - Gone

My wipers developed a similar problem one day. I opened the fuse box, wiggled and pushed in all the relays and hey presto all was well. I now check relay seating as a service item. John
07 HSE Narvick Black
Land Rover Series One
Triumph Rocket 111 (sadly gone!)