this sounds ominous - are the edges definitely chipped/spalled?
Most clay pavers have chamfered edges which helps prevent spalling of this nature - are your bricks chamfered or square-edged?
The reason why this happens is that the bricks move slightly when trafficked and by pressing too tightly against their neighbours, the pressure is concentrated on the edges, which then 'spall'. This, I stress, should *not* happen on a properly laid clay brick pavement, which suggests to me that there's summat amiss with your driveway.
The most common reason for this sort of behaviour is that the contractor has either used an inadequte sub-base, or has omitted it completely. The sub-base is the load-bearing layer of the pavement, and it is absolutely essential as it ensures the individual bricks are capable of carrying the weight of cars, vans or foot traffic, without being forced into the ground beneath.
Do you recall a sub-base leyer being laid? It should be a layer of crushed stone at least 100mm thick, on which is laid the bedding sand and then the bricks themselves.
Take a close look at your drive in the daylight tomorrow - are the bricks chamfered or square-edged? Are the joints filled with sand right to the top? Is there any sign of 'ruts' forming where the car runs over the paving everyday? If you can provide me with the answers to these questions, I'll be able to give you more of an idea of what is happening.