Since you're passing the size into the derived constructor, why don't you just pass it through to the base constructor?

class base
{
public:
    base(size_t array_size):size(array_size)
    {
        p_array.reset(new unsigned char[size]);
    }
private:
    size_t size;
    boost::shared_array<unsigned char> p_array;
};

class derived
{
public:
    derived(size_t array_size):base(array_size)
    {
    }
};