As for the writing in the Forgotten; to me, the main point was to wrap up one of the two season long arcs for Trip, that is, his inability or unwillingness to face the death of Lizzie. It was the culmination of what had been building all season for Trip.
Trip had been trying to put Lizzie's death on the same level as the rest of the people who died in the attack and later, on the same level as fellow crewmen who died. This way, he could avoid dealing personally with Lizzie's death just as he avoided dealing with fellow crewmen's deaths.
By Archer forcing him to deal with that individual crewman's death on a personal level, it also forced Trip to deal with Lizzie's death personally, because as Trip had told us, her death was the same as fellow crewmen. Also, being forced to work closely with the one Xindi (Degra) most responsible for Lizzie's death helped push Trip closer to a breakdown.
So for me, the writing in this episode worked well. That, coupled with Trinneer's masterful handling of the material is what made the episode special.
One other thing, men crying in scenes can be touchy for me. If you show it, there had better be a damn good reason for the tears and the actor had better be able to pull it off realistically and with just the right amount of emotion for the situation. The death of a younger sibling was one of those "good" reasons for man tears. Connor's "breakdown" scene with T'Pol was nearly perfect, understated but full of obvious emotion. I think he even managed to pull a poignant and in-character response from Jo also. But I think the writer and director have to get at least some of the credit here too.
I agree with gblews here. I was a lot closer to grief when this episode aired, and I think I would have had a way different reaction to it if I thought it was in any way fake or manipulative. That said, I would never be so presumptuous as to try to define a right or wrong way to grieve - or give it an expiration date. I think there are people, soldiers in combat certainly, who stuff their feelings into a lock box because they cannot indulge their grief and do their jobs. They wall off that part of themselves because letting it distract them will get them and their comrades killed. But like any container, if you don't let off the pressure a little bit every once in a while, you get an explosion, or, in this case, a breakdown.
I think Trip spent the better part of season 3 in denial - not denial that his sister was dead, but that it mattered more to him than any of the other casualties. In that way he was able to put himself on a par with everyone else in the crew: got a job to do, gonna do it. To examine the Xindi in the light of his own loss would be excruciatingly painful, but also set himself apart from them. Without any other family, he would be alone, trying to deal with the loss. So, he doesn't.
I do believe that Archer knows in Forgotten that Trip needs to write that letter. It didn't need to be done that day; it wasn't going to be sent anytime soon. But Trip need to work with Degra, and he needed to deal with Lizzie to do it.
As for someone showing grief, I think crying is appropriate, but ... Trip has been dealing with it the entire season. Him deciding to cry in this episode felt like, "Hey, you've been upset for nearly a year."
They say it takes a whole calendar year to begin to get over a death. I would say that's true, at least a year. I know for me, two, three, even four years in, I could see a picture, hear their names on the TV, come across a condolence note, read a fanfic story on-line, and go right back to "that place" and cry for hours.
I'd add that Archer showed his grief in other ways - he was so tightly wound that he didn't allow himself to break down. That's a consistent characteristic throughout all 4 seasons. I wish we'd seen him do so in a private moment-type scene in Season 3. (And yes, those were real tears in Archer's eyes when he saw Trip in Observer Effect.)
I think both the writing and the actor's choices in this scene were dead on: believable, resonant, affecting, and not in any way contrived.