Why did naval funding drop off in Byzantium?
Initially, lack of necessity; later, lack of means. After the reconquest of Crete there was no serious challenge to Byzantine power on the sea aside from Sicilian raids on Byzantine Italy. Over the late 10th and 11th centuries, the empire's Muslim adversaries declined or disappeared as naval powers (the Fatimids, Crete, Sicily), while the new threats to the empire were wholly land-based (the Bulgarians, Pechenegs, and Turks). Under such circumstances, beggaring the navy to expand the army made sense, and the Byzantines cut funding, neglected the fleet, and in the case of the Adriatic outsourced their protection to Venice, which at the time was a friendly power and a nominal vassal state. After the loss of Anatolia, the state's revenue plummeted and mere survival on land became essential, and by the end of the century Venice and its fellow Italian republics had grown too powerful at sea to be seriously challenged without a naval revival that the Byzantine state could not afford. The Komnenids, particularly Manuel, made efforts to restore their naval power, but money was always just a bit too tight. Given its dangerous opponents on land, the later Byzantine state rarely had the luxury of building serious naval power, and their attempts in that direction were fitful and short-lived owing to scarce resources.
A late medieval Byzantine naval revival isn't impossible, but the question is one of priorities. An army is always necessary; a fleet is only necessary under certain conditions. I'd expect the Byzantines, like any state, to alter their spending based on their perceptions of the challenges they face. If the empire's land borders are really as secure as you suggest and the greatest threat is maritime, that suggests more naval spending; but nice little empires surrounded by pliant yet resilient vassal states don't tend to stay in such stasis forever. Indeed, a strong army is what keeps those vassal states pliant in the first place, whereas they may not fear a strong navy depending on their geographic situation. Good luck intimidating the Bulgarians with ships.