The pyrolysis of lignocellulosic biomass is one of the most promising methods of alternative fuels production. However, due to the low selectivity of this process, the quality of the obtained bio-oil is usually not satisfactory and does not allow for its direct use as an engine fuel. Therefore, there is a need to apply catalysts able to upgrade the composition of the mixture of pyrolysis products. Unfortunately, despite the increase in the efficiency of the thermal decomposition of biomass, the catalysts undergo relatively fast deactivation and their stability can be considered a bottleneck of efficient pyrolysis of lignocellulosic feedstock. Therefore, solving the problem of catalyst stability is extremely important. Taking that into account, we presented, in this review, the most important reasons for catalyst deactivation, including coke formation, sintering, hydrothermal instability, and catalyst poisoning. Moreover, we discussed the progress in the development of methods leading to an increase in the stability of the catalysts of lignocellulosic biomass pyrolysis and strengthening their resistance to deactivation.