I bought Diaspora recently, having very much enjoyed Don't Rest Your Head and being a huge fan of harder Scifi. I'm curious how well it holds up to play by post gaming compared to something like Shadowrun or D&D. If it is not suitable, how so? Can modifications be made to increase suitability?
Absolutely. Diaspora is a Fate based system. Fate is "rule lite," story oriented, and uses minimal dice (called "FUDGE" dice) and character statistics. That makes it uniquely suited to online play.
While there are still dice involved, the game does not revolve around your dice rolls and pure chance. D&D, Shadowrun, and other games that follow a more "board game" style mentality usually require more interactivity. Looking over peoples shoulders for their dice rolls, game maps, et al. While rules-lite and story-heavy systems, such as Fate, revolve around story. You could potentially pull the dice entirely, and it very well might not change your game very much. If at all. Assuming all your players have a sense of fair play and continuity.
It usually pretty easy to find games on official forums for indie games like that. You might want to check out Diaspora's forum if you are looking for a game, and looking for even more specific feedback about that particular game.
There are several places in the rules where they defer to "social initiative", which is just "whoever speaks up first". I point this out because this is incompatible with play-by-post, so looking for these cases and considering how to manage them differently will help the game go smoothly. In particular, the space combat minigame uses social initiative.
There are very many parts of the rules that defer to table consensus. This deference works in person because complicated and nuanced discussions can happen fairly quickly. These come up in rules interpretations before play and in rules application during play since the rules are written loosely assuming table consensus will determine how to handle unusual circumstances particular to your cluster and your sessions. In play-by-post, such frequent tangents to sort out a ruling by consensus during play ("Can I use Charm on the Tech 4 AI? Why or why not? If I had Military-Grade Charm would it work on machines?") could blow up into huge, recurring derailments and is probably something you want to avoid.
For these, the immediate solution I can think of is to simply claw back that authority from the table and give it back to the referee. However, if you have a side-band communication method like a busy OOC board or instant messaging, perhaps you can maintain some of the consensus but limit the length of discussions, with the referee deciding when the discussions are unresolved.