"Missi dominici" weren't much of a system to begin with, than being a more or less informal function from Merovingian and early Carolingian times : trusted royal agents being sent to validate, control or negotiate obedience from local Frankish elites or nobility; managing a situation in particular.

Early Carolingians resuscitated this practice, and Peppin III even systematized it in all the regnum as part of an effort to rebuild a public service (that had collapsed in the VIIth century) and hierarchical authority against the aristocratic abuses. But the aristocracy itself had become significantly entrenched thanks to landed holdings and regional networks, and while the social recruitment of Peppin's missi into his personal vassals technically prevented them from falling under aristocratic influence or corruption : as missioned agents were also under a formal scrutiny from the Frankish aristocracy where they were sent and not just from the king, in spite (and explaining) the important legal protection they received from him.

Charlemagne's decision in 802 could arguably be described as a first institutionalisation of this function, with missi no longer being limited to a single task but being trusted with a territorial mandate known as missaticum, effectively intermediary between pagi and the palace. But no longer missi were personal vassals from the king : rather, they became recruited into the same aristocracy they were tasked to oversee. Various reasons are proposed for that, chiefly that it prevented corruption of the royal agents but reinforcing the prestige, authority and efficiency of these royal agents by confronting local aristocracy with peoples from the same standing or even local origin than themselves (most of missi in this period acting in their own homeland) which seems to have been efficient enough and especially for clerical missi (which eventually became a favored recruitment poll), but eventually depended on the prestige and authority of the palatial and royal authority. And while clashes between these and the aristocracy were fairly rare under Charlemagne, it is both thanks to his important prestige but as well his reluctance to act against regional power of the potentes : missi were fairly absent of southern Gaul and peripheral territories at least until Louis, and really efficient in the lands closer to the emperor.

Louis himself seems to have done his best to systematize the power of missi in his realm, favoring clerical recruitment and systematizing missatica as the immediate level of hierarchical display and administrative management above nobility as a whole. But beyond appearances, missi weren't public servants as much as trusted aristocrats forming an ever-narrowing social-class closed to petty-nobility or vassals. Thus, the appearance of a bureaucracy was rather set into the conflicts within Frankish aristocracy (from which Carolingians never really managed to get out from) and the general crisis of Carolingian Francia.

With the decline of royal authority face to their aristocracy in the late IXth century, these pretenses effectively disappeared, but not the function or title of missus itself. Late Caroingians having to directly deal with an aristocracy jealous of its standing, and in a much weaker position than their predecessors, still benefited from the prestige of Frankish honors granted by the king (to the point a differentiation was acknowledged in the late IXth between the regnum at large and the king) they could grant to strengthen or shift loyalties, "public function no longer seen as a delegation of power but as the salary of personal loyalty" (Bruno Dumézil, Servir l'Etat barbare dans la Gaule Franque; Tallandier;2012)

As such, Frankish potentes required kings to name missi, even requiring that they'd be settled/landed in their missatica if they weren't already. These of course didn't control much, even less functioned as a hierarchical layer between the king and his aristocracy (that more and more assumed the mantle of an oligarchic counter-power, with claims to imitating the old Roman republic) but remained a staple of the unstable and blurry at best hierarchisation of an increasingly "horizontal" upper society.

Eventually, it's not that Carolingian "discontinued" the use of missi : it's that their whole state was built on difficult relations and power-balance with aristocracy they couldn't keep the upper hand on.