There's no good time in-season to change managers when the team is involved in midweek competitions. If you leave it to an International Break (IB) and most of your 1st team squad are internationals (as is the case with us) the new manager has little to work with. The advantage, though, is that he can at least work with some of the squad for a reasonable period to explain his system and those away on International duty are at least likely to be told what system they can expect to come back to.. We have 4 games before the next IB (Fulham, Spurs, Hoffenheim and Liverpool). Two of the first 3 games after the IB are crucial league games against Coventry and Hull[; the other, a home game against Real Sociedad who are likely to beat us whoever's the manager.
If you do it after a game with no following IB, then the new manager has just a couple of days before the team has to play again. He might hand the responsibility for that first game to whoever is left of the coaching staff (in our case probably Paddy) so that he can focus on watching the game and make decisions about what he sees.
If the club are to sack Sage and bring in a new man (no, I'm not being sexist here, we won't be appointing a woman) then IMO it has to be no later that the upcoming IB. If he's not gone by then, I would expect him to carry on till December and if things haven't improved he'll be sacked so that the new man will have some time before the January transfer window opens.