Continuous play bonus.
Example:
Get a 50% rep bonus for every consecutive strike played. Max bonus of 200%. So only takes 4 (after your first) games to get full bonus and then every strike you get 75 rep (90 if you did nightfall).
Can make it such that getting disconnected due to an error will not remove your bonus for X period of time (say like 30 minutes). So if you get disconnected you can hop back on but you cannot force an error and then come back the next day with your +200% bonus.
This would be a huge boost to players who are trying to up their rep for shaders while also giving people an incentive to play every strike. It will also help increase the rewards by increasing the speed you lvl up factions.
Edit: love the responses guys keep them coming. My personal opinion is rewarding players gets you better results than punishing players as punishments just lead to gamers not bothering to play at all.
Edit2: For those saying the pole is bias. I was not attempting to create a pole asking people if they want rewards or punishments. But rather wanting to see peoples thoughts on this specific idea. If you want rewards but dont like this option the "I do not care" button was placed for you.
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Some people already feel like the game punishes them by repeating strikes and not rewarding them for their continual play. I stopped playing Halo because of loosing good rep and earning bad rep due to a poor connection. So yes let's do this in destiny too, but also make a pvp mode where you can take all of my gear too. I can come join your session and you can shoot me with all he best weapons in the game and take my crap that's probably just shards to you anyway. Personally, I like the fact that "GashGrabrr435" is able to quit out, I stopped reviving him 2 Omniguls ago anyway. I got the feeling he didn't like getting paired with chicks since he kept running ahead and never revived us.