In the end, the likely scenarios are that they either stay in H!P for so long with the remaining members that they are elevated by their own legacy (ala Cute), or a second generation will be added. Neither of which will guarantee further progress. There almost always seems to be a certain level of stagnation that happens two or three years out from a group's debut, and it usually takes a concerted effort or major event to change that. Juice=Juice had one, S/mileage, Country Girls, and while they were overshadowed by the recession, both Berryz and Cute had theirs as well before things started to swing around. Kobushi was just unfortunate to have started theirs in conjunction with an assortment of member issues after nearly a year without a Single release, topped off with other groups, transfers, debuts, and news of future units to divert attention of the fans elsewhere.
Right now the momentum may be with Tsubaki, and they may be fortunate enough to maintain their own momentum for a bit longer than is common for H!P groups, but management will eventually do something for Kobushi. Tsubaki having so much momentum has the potential to stoke the fires under the feet of the Kobushi members as the agency starts pushing the underdog narrative for them as they did with S/mileage when they were told that Juice=Juice may get their first Budokan and leave them behind if they weren't careful. In a similar fashion to the Year of Cute, all of the events around S/mileage for the next year+ brought momentum back to that group even before the introduction of new members and the name change to Angerme. At a future date, we could see the start of the Year of Kobushi, for all of the unknowns that it may entail.
Although it has unfortunate implications for how it toys with the confidence and dreams of the members, I tend to look at decisions and events in H!P as if it were being booked in the style of a wrestling promotion. More often than not, it plays out very similarly even if it isn't always quite so dramatic or if the drama isn't always intentional. Kobushi started strong, people got used to them, other interesting stuff happened, and now they need to work their way back into the spotlight themselves or be given another push. It's a compelling story that sells tickets.