They fell behind because Japan was united under one government, and that one government (a few early rebellions aside) prioritized maintaining peace and order over military development, and underestimated the threat of foreign nations in the early 19th century. Japan advanced in many ways, culturally and economically, during pax Tokugawa, so to speak - by the 1700s Japan was highly urbanized (for pre-industrial society), with Edo growing to be perhaps the largest city in the world. It had a growing middle class and a thriving artistic scene. What it didn't have was war - something that hadn't been the case for the period that predated Tokugawa rule. During the Sengoku period, Japanese warlords came to field highly sophisticated armies - world-class, for sure - with large numbers of matchlock arquebuses, both imported from Europe and manufactured natively. After the Tokugawa clan secured their domination over Japan, however, they clamped down heavily on firearms manufacturing and trade (as well with most foreign trade in general) in order to keep peace and order.

In the early 1600s Japan really wasn't that far behind the West when it came to the manufacturing of small arms. They didn't produce heavy cannons in great quantity, but that was more due to a lack of need than the lack of ability. The answer to "how did Japan fall behind so far in military technology" is really just that they didn't try to keep up with the development of military technology that was going on abroad. They had limited exposure to western developments through their contacts with the Dutch - something known quite literally as "rangaku" - Dutch learning. But most people involved with rangaku focused on areas of technology that weren't of a military nature. After all, Japan was at peace. The Tokugawa Shoguns seemed to have been largely convinced that Japan would not be put under significant threat from abroad - after all, they had succeeded in halting quite a bit of European contact with Japan without any serious European pushback, and they had secured one European partner in the form of the Netherlands.

By the time western ships started appearing off the coasts of Japan with some regularity there were some Japanese individuals who did seek to advance Japan's military capabilities. Some Japanese gunmakers experimented with air guns, whilst the samurai Takashima Shūhan imported flintlocks and other modern arms, as well as military manuals, through dejima - the artificial island at Nagasaki that served as the sole trading post with the Dutch. The bakufu - the government of the Shogun - took an interest in Takashima's plans but eventually individuals who feared his influence had him put under house arrest for subversion and treason. Other modernizers were similarly ignored by the bakufu until the arrival of Admiral Perry spurred rapid attempts at military modernization. Before Perry, there were simply too many bakufu officials who saw more modern weapons as either not particularly effective or just not particularly necessary, and the internal struggles of the late-Edo period government definitely hampered modernization, despite the fact that the required knowledge was present in Japan thanks to their connection with the Dutch.