Because he seems to be the workaholic type, who only bothers with his own work and nothing else, aka., like a typical Japanese office drone.
I mean, if you leave your fiancee alone just after her father died with the excuse that you had to manage the store to stop it from collapsing, then you seriously have some issues.
How much time per day would it have taken to manage the store realistically. He could have easily went and looked after his fiancee after store closing hours. Is he saying that he also gave-up his night and sleep to save the store? That's kind-off unrealistic in this Medieval setting.
Plus, it's standard in many regions to close down the store for a few days if the Owner of the store had expired even if it's in financial crisis.
And if you don't want to waste time by not even taking part in mourning and supporting your fiancee through her grief just because of work, then it's more of a skill issue than something else.