Their craziness doesn't matter. Usually crazy customers aren't rich. So if you build to their craziness, you'll lose the customer.
You need to build an appropriate infrastructure that will win the bid, figure out what you can achieve (99.9%/99.99% uptime) and build in enough overhead to cover your SLA penalties. Or negotiate a monitoring methodology that is in your favor. (ie. exclude planned maintenance windows, use a monitoring threshold/interval to allow you to address issues before triggering contract "downtime", exclude external provider issues, etc)
On a personal level, I think individual people who've become wealthy have a more reasonable outlook when it comes to stuff like this, but this doesn't apply to rich _companies_.
The least reasonable clients I've ever had were employees of large companies, and more specifically those who'd been recently empowered with the responsibility of the project I was working on and lacked the perspective required to realize that crazy doesn't help anyone.
It's not their money, but it's their decision, and that's a petri dish for crazy.
You need to build an appropriate infrastructure that will win the bid, figure out what you can achieve (99.9%/99.99% uptime) and build in enough overhead to cover your SLA penalties. Or negotiate a monitoring methodology that is in your favor. (ie. exclude planned maintenance windows, use a monitoring threshold/interval to allow you to address issues before triggering contract "downtime", exclude external provider issues, etc)