They typically won't in the context you have laid out.

Typically the reason this is done is to save money (Sometimes in the thousands when considering Int'l business class tickets) and it is United as well as every other airlines policy to get you where you are going safely and as quickly as possible. However, the second flight is no different than missing a cruise or a meeting, that is not their concern.

Now, that said, sometimes they have some leniency and will help you get to your destination. One of my first Int'l flights was booked in this manner due to "Corporate" wanting to book all Int'l flights and it was over a weekend, I ended up in the wrong city and no one was available to rebook, so I had to fly to IAH to take the flight. The ORD-IAH plane went maintenance and I missed the flight. Cust Service in ORD re routed me on the direct flight to HKG. So, there is hope, but the fact I was scatter brained and it was a maintenance issue probably helped significantly.