Well, he doesn't really "have a total meltdown" after Rose dies, but he does withdraw into himself for a season or two, but everyone needs time to get over a loss,
A season or two is a long time to a mouse:
Matthias and Cornflower have Mattimeo at the end of the Summer of the Late Rose (let us ignore the biological difficulties with such a feat for a moment).
Therefore, at the beginning of
Mattimeo, Mattimeo is eight seasons old: no longer a dibbun, but not quite as old as Matthias is at the beginning of
Redwall. An eight year old human child would be incapable of the feats that Mattimeo performs, so the intuitive ratio of one season to one human year is unavailable; Perhaps two seasons equal one human year. Jacques effectively said as much during a book signing in his twentieth year of writing, "I've been writing books for forty seasons," so my proposed ratio holds.
Therefore, if two Redwall seasons equate to one human year, Martin withdraws for almost a year. Such a withdrawal is not only above normal for humans, but for Martin himself because plenty of his fellows die throughout the book, yet he only breaks as badly after Rose's death.
especially when the person who died was your true love,
Eugh. "True love," my rump. No such thing exists. (I know full well that I sound grumpy and ornery in saying so, but no two people match each other perfectly).
and she died saving you,
I thought that she just died in battle while Martin watched. If you have a copy, then I'd like to see a quote just to be sure (and, of course, to enjoy Jacques' beautiful prose once more

).
and you have faced plenty of other deaths in your life,
But his nigh nonchalant experience of other deaths is precisely what bothers me when I attempt to understand his breakdown over Rose's death. If they affected him enough to weigh upon him, then he
should have broken down slowly, not all at once.
but I think that Martin deals with it pretty well, at least he doesn't brood over it for the rest of his life and never ever recover.
He does brood over it for the rest of his life, and he never recovers: he never falls in love again.
-Duxwing
I wouldn't say that just because he never loves again means he never recovers, many people either only love once, or never love at all, and it is not always because of a previous tragedy, but because they don't find the right person.
And I don't think he broods for the rest of his life, I mean, it still makes him sad and probably angry to think about it, but I think he accepts it and moves along.