The pre-war importance of Basilisk Station
Combination of factors at work here.
(1) King Roger is still alive, and the Admiralty kept a considerably heavier force either in the Basilisk System itself or "on-call" at the wormhole junction during his lifetime. Please recall the distance between the Junction and the inhabited planets of the Manticore System; any ships stationed at the junction where they could make rapid transit to Basilisk were badly out of place to cover the core planets, so a simple "detachment" from Home Fleet did not suffice for that purpose.
(2) Honor is approximately 20 at the time of Ms Midshipwoman Harrington; she is forty-two at the time of OBS. In the ensuing 22 years, there was plenty of Time For Changes with the "new" deployment policies for Basilisk having become "established policy" long before OBS. In fact, the Basilisk detachment was systematically downgraded in part because of the build-up vis-a-vis the Peeps (see below).
(3) The size of the Navy available at the time of MMH was substantially less than that of the time of OBS. In other words, the picket force stationed there (and earmarked for quick reinforcement via wormhole) was a larger chunk of the total forces available.
(4) Aside from Trevor's Star, Basilisk was at that time the only strategic point threatened by the PR. Moreover, it was the SKM's only extra-system possession, which elevated it to a special status in Honor's thinking.
(5) As the situation WRT the PRH grew progressively more nasty in the 22 years between MMH and OBS, Basilisk -- because of its astrographic isolation from the frontier with the PRH -- assumed a lower and lower strategic priority, even for those who felt that the Janacek-level pickets were much too low. The theory ran that since we have limited resources, and since we are busy assembling an alliance to secure our frontiers, we must spend the ships we have (and can spare from Home Fleet) picketing/protecting our frontiers (and our allies thereon). Basilisk, while potentially extremely useful to the PRH in several ways, is much further away from any of their advanced bases. Moreover, it, unlike any of the systems between us and them, is actual Manticoran territory, so any attack on Basilisk would be an outright act of war, thereby triggering all our other forces closer to their frontier. This means they are actually less likely to attack there (dispersing their own naval unit over a wide operational area) than to attack the forces we have made concentrated targets by picketing allied systems closer to their frontier. Because of all of this, we do not anticipate their launching an attack in the Basilisk area without first making substantial changes in their own deployments. Once they begin moving in that direction, we can quickly reinforce from the home system if we have to via the wormhole terminus. Please note that there are some mutually contradictory aspects to this particular piece of logic, but that's pretty much par for the course in this sort of situation.
By the time of OBS, Basilisk had been the "dumping ground" of the RMN for perhaps fifteen years (long enough to seem like forever even in a society with prolong, when you think about it), but the rationale for why this was so had altered steadily over that time span. This resulted from both reasonable and unreasonable logic chains (see above) and also from the fact that whatever the size of one's picket in a system, one would seldom "waste" the talents of one's more capable officers in patrolling a system whose strategic importance was questionable and which one might yet find one's government deciding to give up. In the case of someone like the RMN, in particular, with hot-button frontier systems on one side of its operational sphere and heavy-duty pirate suppression duties on the other side, this is particularly true.
What was changing by the time of OBS, and what Janacek was busy ignoring, was that the Peeps had begun to move towards Basilisk, as their later establishment of bases at places like Seaford indicated. He was "behind the curve" on readjusting fleet deployments in the face of changing threats (partly because of his own hostility to anything which smacked of interstellar expansion ... which Basilisk typified), and, unlike certain previous Admiralties, he saw Basilisk not simply as a system whose security could be entrusted to his less than stellar officers but as a place to send someone in order to tell them that he thought they were an incompetent jerk. In other words, it was Janacek, more than anyone else, who had deliberately turned Basilisk into a "punishment station," and he had done so for multiple reasons.
As of MMH, all of this lay several years in the future. Midshipwoman Harrington is explaining to her fellow middy using the best, most current example of the SKM's expanding responsibilities in areas other than Silesia.