I was in a situation where there wasn't one person doing this, but a relay of people in different departments in the organization - they would each come down and 'visit' with me, insisting that their project get priority.
Most people here are inviting you to tell the customer 'get lost', and I'm not sure that's productive. From the perspective of the user, the two separate issues are finding the boss in the first place (s/he may not be responding to the customer's communications), and the second is perceiving the boss as unknowing or unhelpful. You might have a pushy client that is just rubbing everyone the wrong way, and is making demands on time that can't be met. You may also have a client that feels stranded, and this might be a legitimate conclusion.
First you have to figure out whether the customer's expectation is excessive, and whether the boss is doing his/her job. If the two answers are both no, then the right approach is to simply keep the boss in the loop, and deal with the customer until someone overrides your decision. In departmental and company meetings, you should point out you're handling customer interface, which might create an embarrassment for your boss, but on the other hand everyone else may already know what s/he thinks of this customer. Being good at customer relations is an asset - it doesn't hurt to have a rep in that regards.
(Note: in the 1970s I actually took a phone call from a belligerent customer, and everyone else in our bullpen could hear it, including my supervisor. This guy chewed my ass for a good half hour. No one had any inclination to intervene. Perhaps this was viewed as an exercise in character building.)
If the customer's expectations are excessive, then you can either ignore the phone call, or respond very slowly. If the customer wants something now, figure out how long it would take to do it if normal channels were working, and deliver it slightly later than that. In short, figure out whether you are the path of least resistance, and increase the resistance until you aren't.
There might also be a way to communicate with the boss about the situation, and see if the calls can get routed through a sales rep, marketing, the customer's boss, or some other more circular route that makes more people aware of the sore point. If there is a trust issue between your employer and the customer, it might be a good idea for the two of you to go your separate ways. It isn't that easy to tell from the details provided what the bigger picture is.