Why did Mozi's philosophy die out in China?

I think there are these reasons:

• Around the time of its decline, Chinese philosophy was quasi-religious, and exclusionary. That is, Mohism was actively suppressed by regimes that adopted other philosophies, such as Confucianism.
• Some of its doctrines became obsolete
• Some of its doctrines were absorbed by the other philosophies

Exclusion

Mohism arose during the hundred schools of thought, a period of time when China was fractured with no strong central authority, so many different philosophies/schools flourished and competed against each other. This came to an end when Qin unified China, and Qin adopted Legalism, to the strong exclusion of other schools. The most prominent example of this violent exclusion was the burning of books and burying of scholars (焚書坑儒), which wiped out most of the schools and would have done the same to Confucianism if Confucius's works weren't later found hidden inside the walls of his residence.

Later when the Han dynasty adopted Confucianism as the state philosophy, it too suppressed other philosophies, and although it was by far less bloody than Qin's efforts, it was still marked by some palace intrigue. What was unique to Mohism however was how strongly its doctrines were in conflict with Confucianism; its focus on impartial meritocracy directly contradicted the Confucian concept of filial piety, where loyalty to one's family and elders was paramount. Another point of conflict was over the role of rituals, which were considered useless by Mozi but of strong importance by Confucius.

Obsolescence

Mohism valued things like logic, mathematics and pacifism. The first two in particular meant that the best siege engineers were Mohists. This meant they were highly sought after during the Warring States period.

This all changed after China was unified; what warfare was left was mostly limited to suppressing bandits and defending from nomads, none of which required engineering expertise.

Absorption

Perhaps the greatest reason why Mohism died out (and other surviving schools, like Taoism didn't) is that its best doctrines were absorbed by the prevailing philosophies and what was left was a pile of unattractive theories. Let's look at its ten doctrines in detail:

“Elevating the Worthy” and “Conforming Upward”

Mostly absorbed between Han and Tang dynasties, although with a strong Confucian twist. A meritocratic imperial examination system (科舉) was set up, although a huge portion was devoted to the study of Confucian classics. A quasi-meritocratic system of civil recruitment (孝廉) was adopted by Han, where (in theory) this avoided nepotism, but candidates were judged on filial piety and virtue (incorruptibility) instead of talent and ability. Made more meritocratic by the Tang dynasty when this system was abolished in favour of the imperial examination system, arguably the most meritocratic in the world in its time.

“Inclusive Care” and “Rejecting Aggression”

Although the impartiality and pacifist aspects weren't absorbed, one key element of these doctrines is basically the Golden Rule, which is shared by virtually every major human philosophy.

“Thrift in Utilization” and “Thrift in Funerals”

Thrift (廉) is a strong Confucian virtue, although the two philosophies differ on rituals (such as funerals). During the Han dynasty, officials were required to resign their posts and mourn for three years upon the death of a parent or grandparent. In theory, reducing the expense of these rituals would be hugely attractive, but it also became a useful political tool to slander officials who infringed on the mourning ritual, notably Bai Juyi who was exiled partly due to writing poems during the mourning period for his mother. As we all know, once something becomes a political tool, it can be exceedingly hard to get rid of.

“Heaven's Intention” and “Elucidating Ghosts”

This focus on mysticism and religiosity notably does not prescribe any specific targets of worship, and hence is compatible with many other philosophies. Arguably it conflicts with the areligious Legalism, but then again it was not a state philosophy by the time of Han.

“Rejecting Music” and “Rejecting Fatalism”

Strong conflict with Confucianism, but the rejection of music and other "idle" activities made it unattractive to the kind of rich patrons that could have greatly promoted Mohism.