The forecast of electrical loads is essential for the planning and operation of the power system. Recently, advances in deep learning have enabled more accurate forecasts. However, deep neural networks are prone to adversarial attacks. Although most of the literature focuses on integrity-based attacks, this paper proposes availability-based adversarial attacks, which can be more easily implemented by attackers. For each forecast instance, the availability attack position is optimally solved by mixed-integer reformulation of the artificial neural network. To tackle this attack, an adversarial training algorithm is proposed. In simulation, a realistic load forecasting dataset is considered and the attack performance is compared to the integrity-based attack. Meanwhile, the adversarial training algorithm is shown to significantly improve robustness against availability attacks. All codes are available at https://github.com/xuwkk/AAA_Load_Forecast.