WordPress work not complete but being charged thoughts?

Thoughts on the below I'm currently going through

Requested work through peopleperhour

agreed on the work to be done and was charged a day rate and I paid 50% for the work to begin

half of the work has been delivered and I have been told the other half cannot be completed due to limitaitons of the theme etc, But they want the remaining 50% to be paid as they spent time investigating if it could be done or not.

Would you pay that final 50% without the work being complete? Am I being a complete idiot for even thinking that