It is not an issue with "captains" per se, but investment, available resources, ownership structures and patterns, and with player power (and concomitant lack of loyalty) in clubs that are no longer deemed as attractive as they were.
Arsenal have many issues, the main one is that - because of their brittleness, erratic form, and the notorious defensive frailties that they have failed to address - they are unlikely to qualify for the Champion's League, and that, in turn, makes playing for them less attractive.
They need to invest in (and build) a decent defence; that is where progress (and confidence) will come from.
Koscielny's conduct is inexcusable, of course, irresponsible, disloyal, discourteous and he deserves to be stripped of the captaincy at the very least.
However, as has been the case with other clubs, once a player has made his mind up to depart from a club, irrespective of his contractual obligations, it is hard to retain his interest in and commitment to his club, and probably best to sell him of the best price possible as soon as possible, for such a disinterested and dissatisfied (and demotivated) player can only serve to become a disruptive and negative force in the dressing-room in the sort-term if he stays.
