While not an expert on contemporary Mexican history, I may be able to help you. In my opinion it has to do less with the figure of Maximilian himself and more so with local situation. Commonly, the 19th century is known in Mexico as “el siglo del desmadre” (the century of chaos, in colloquial Spanish). This is because of the uncountable number of levantamientos (local upheavals) and pronunciamientos (uprisings) that took place at the time. Basically, to sum things up, Mexican political life was a complete disorder, particularly with two opposing views; on one hand the liberals trying to promote a federalist government, and on the other the conservatives looking to impose a centralist government. Among the conservatives, there was a group that liked the idea of a monarchist government, a la Europe. These parties clashed harshly during the Reform war in which the liberals won, but the Mexican economy took a major hit, rendering the payments of foreign debt an unfeasible undertaking. This situation was taken as an excuse by the French to invade Mexico in what is called the French Intervention of Mexico. During this time, the conservative elite, particularly the monarchist group, saw the perfect opportunity to establish a Mexican monarchy and thus they created the Second Mexican Empire. This is why they bring Maximilian. So, at the beginning of his reign, Maximilian had the support the French troops in Mexico and the conservative (also known as monarchist) party. However, Maximilian turned out to be more liberal than conservative to the point of upholding some of the leyes de Reforma (Reform laws) that had catapulted the Reform war. It is because of this that he lost the support of the monarchist in Mexico. At this point, the US civil war had ended and the US government provided some support to the Mexican liberals, head by Benito Juarez, to try to push French troops out of Mexican Territory. Once, Napoleon III decided to leave Mexico, Maximilian is left without the support of the monarchist and without the protection of French troops. Once the liberals were reinstated into power, (a period known as La Republica Restaurada “the restored republic”) Benito Juarez and the liberals killed Maximilian as a statement that Mexico will not tolerate the imposition of a foreign power. After this, the reformist agenda continues with Juarez changing few of Maximilian policies since both men had similar ideas. I hope this helps in your inquiry.