Software Is Not Like Making Shoes

Your team has been struggling for weeks with no solution in sight. The software seems ok. The HW is perfect. But the software is not behaving correctly in a particular mode for a given set of condition. The team is working day and night. Being a good PM, you have ensured that the customer is in the loop. They understand the situation but need the software the following week. You get a call from the customer. You explain the problem but they make it clear that it is your baby and that it is your responsibility to deliver the goods. You talk to the team. They say that software problems are like this. The solution may be trivial but it takes time to figure out what is the problem. This is not like making shoes. This is software. You need the team to kill the issue. The team is getting tired. They think this could be a problem that cannot be solved. The customer is acting difficult.

What do you do?

What do you do?

PS: My views here:
Determining Responsibility