Please be empathetic to people who do not understand what is going on, but who have tremendous responsibility to the business. The business problem is always a superset of the technology problem.

Yes, of course you aren't able to fix it while you are on the phone with them. A conference call will not fix the code. They know that too. But they also need meaningful information and updates in order to do their jobs, which often requires them to provide updates to others like important customers, shareholders, the CEO, or even the government. They may also need this in order to plan out other activities.

Providing useful information and frequent updates (not "contractual" updates) to them with this in mind would go a long way toward solving the whole business problem that is created by the technical problem. It might also get them off your back sooner, and with more respect for you.

There are two critical pieces of information that would help an executive very much: Do we know what the problem is? and Do we know what the solution is? A simple yes/no on both of those would be a great start.