When people join a PbP, they're excited. They can't wait to start. If their characters are brand new, this is doubly true. As soon as the GM drops the first introduction post, every player usually posts within the same day.
The first week into a PbP has a similar level of posting going on. So long as the GM keeps up their daily post, the players will too.
By the second week, the scenario may have hit a steady state. Players won't post unless the direction is somewhat clear. There's a world of difference between tabletop play and play-by-post. There's no side dialogue players can quickly have with each other on these forums, so it isn't always clear what the party's intentions are. Maybe one person wants to talk to the NPC and the other wants to kill her, but neither of them want to step on each other's toes.
Days pass. No one has posted. You post again, hoping to get someone to post. One of the more active players posts. No one else does. Another day passes. You lose interest because if the players don't care about the game, why should you? Hopefully, one or two of the players are keen on driving the story forward, while the rest may usually just be waiting for a chance to 1) engage in combat, 2) be prompted for skill rolls.
With faster PbP games, everyone is constantly checking, updating, roleplaying, and having fun. If you can establish an understanding with your group that more than 2 or 3 posts per day are needed, I can guarantee you that your group will be a lot more interested and effective. That, and they'll blast through a scenario so quickly, not only will completing it feel like an accomplishment, doing it in such a short amount of time will.
With longer, more slow-paced games, it's important that one or two of the PCs interacts directly with the other PCs, or otherwise drives the story forward by hooking onto important plot elements or key terms and hints.
I'm reminded of some classic computer RPGs where certain terms and places would be highlighted or underlined on screen in an NPC's dialog, and those terms would later become part of your adventuring journal. I believe this is something missing in PbP, so taking notes is important. Personally, I keep Obsidian (a note-taking application) open, and keep track of things. It may seem like a lot of effort, but you get back what you put in.
These days, I no longer have time for fast games, and I do fully agree the general "1 post a day" rule is much more applicable to most people's busy lives.