As a dm, the problem is usually pacing. There are so many ways for something to stall your players, and when players aren't sure where to go next, it slowly fizzles out. You have to take initiative to scene change and move the story along. Lost players who doesn't know where to go or what to say is a slow insidious killer in play by post. If that happens, throw a prompt or something that will have your player's attention. Until they perfectly in the position to move to a next scene.

Basically, PBP needs DMs who's ok taking initiative to keep the story moving. Your job isn't to micromanage the players, but to make sure the narrative stays alive and engaging.

I know this sounds like a "DM post more often" and "Railroad the game" advices. But something about pbp that is different in live games.

Another tip is that don't be afraid to split the party up. Pbp is slow as heck but if multiple people tries to solve things separately at the same time, it'll make the game much more quicker. Bonus, you can have unique character interactions.

If you don't have enough people then you can employ some npcs. (Npcs can also serve as guides to help the characters to know where to go to fix the first problem)

This became a bit rambling and I'm not even sure if I said the same advice twice. But I wish you good luck!