A crude model of the UTE is used simulate the pressure field created by the car as it travels through atmospheric air. We must determine the pressure in truck bed because it applies force on the surfboard. The car travels at a constant $60 ~\text{mph}$ (an arbitrary, worst-case value).
UPPER: The velocity profile of air flowing around the car.
LOWER: The relative (to atmospheric) pressure profile and surface plot.
The position of the surfboard greatly affects your answer. I assume the surfboard lies flat, entirely within the truck bed (with the tailgate up). For now, we assume horizontal forces on the surfboard are negligible. Summation of vertical forces will determine whether the surfboard will fly out.
Pressures act on the upper and lower surfaces of the surfboard. The relative pressure profile at the bottom of the truck bed (lower surface) is shown below. A similar profile exists along the top of the surfboard. As a simplification, average relative pressures are used to sum forces on the surfboard, where $P_{ave,lower} = .02 \ ~\text{psi}$ and $P_{ave,upper} = .03 \ ~\text{psi}$.
Various surf websites list short-board dimensions and weights, where $A_\text{surfboard} \approx 2100 ~\text{in}^2$ and $W_{surfboard}\approx 6~\text{lbf}$. At $60 \text{mph}$, the resultant forces due to pressure are:
$$F_{lower} = A_{surfboard}P_{lower} \qquad \text{and} \qquad F_{upper} = A_{surfboard}P_{upper}$$
$$\therefore F_{surfboard} = (F_{lower} - F_{upper}) - W_{surfboard} \approx -27~\text{lbf} $$
Therefore, your surfboard is held down by $\approx 27~\text{lbf}$- Your surfboard apparently testifies to this! As other answers indicate, there are other considerations. Accelerations and transient effects are unknown. While your surfboard appears to be safe at constant speeds, you should remain wary and assume that it could go flying.
This model illustrates two types of fluid flow (Flow Regimes): Laminar flow characterized by 'smooth' profiles, and Turbulent flow characterized by 'chaotic' profiles. Mach flow exists when a fluid's velocity is greater than its speed of sound ($c_\text{air}\approx 761 ~\text{mph}$), creating a shock wave- it is not relevant in this problem. *Note that turbulence and road chatter are likely responsible for the surfboards "shifting".
Flow simulations (CFD) are the most accurate way to solve this type of problem, but since you are interested in theory, consider an idealized (less accurate) model of flow: Bernoulli's equation, $\Delta [P + \frac {1}{2}\rho v^2 + \rho g z] = 0$. It relates pressure and velocity so that an increase in velocity decreases pressure. This is seen comparing the flow simulation's velocity and pressure profiles, most apparent on the roof where velocity is high (orange) and pressure is low (green). It is impractical to apply the Bernoulli equation to this problem because neither the velocity or pressure are known as they flow over complex geometry. Additionally, it assumes incompressible fluids and does not account for turbulence.
