Hypothetical scenario: what if this were a part of a longer route? For instance, OP lived in Anchorage, Alaska, but had to travel to Houston as part of his business trip. From there, he is taking another trip to DEL and back to Houston for a week or so, and then back home to Anchorage?

Let's assume that the luggage was lost in IAH (on the inbound), and the OP had to stay in IAH for work for another week or so?

Can the airline still deny refunding?