Farming isn't effective?

Does repeatedly farming a boss give reduced rewards?

I've noticed while running through Terramorphous and The Warrior over and over, the drops are getting worse each time. By worse I mean any color of drops are getting rarer and the total sell value keeps going down as well.

After beating the boss and looting everything I just do a save quit, then continue.

No, there is no such thing as deteriorating drops.

From the dawn of time there were legends of subtle dependencies and rituals, that help a player boost his chances at games like Borderlands. When I was young, I had to convince my friend that shutting down Diablo 2 and restarting it does not boost his loot quality in Baal runs.

Of course, your theory makes more sense than dependencies like that one, but it is still wrong. It is just an unlucky streak and the way humans perceive randomness. Cognition is always working through expectation, and when you come up with a theory, your brain starts picking up evidence of it being true and ignoring conflicting facts.

The only way to check it for sure is to keep a list of every drop, color and price, and look at it when it becomes long enough - say, a hundred runs, but a thousand is better. Any sample less than a hundred would be random and would not demonstrate tendencies and chances.

Farming definitely works. I've heard rumors that some bosses give better drops the very first time but I think it's BS; several people have suggested X boss always drops Y legendary the first time, but I've never found this to be true (however I've had Boom and Bewm drop the Bonus Package twice on first runs through different playthroughs).

Particularly with Terramorphous and Bunker I've noticed there seems to be an explicitly set number of green or better, blue or better and purple or better drops. Legendaries are however much rarer than they were in Borderlands, so if you're basing your expectations off of BL1, especially Crawmerax's drops, you'll be disapointed. Legendaries drop at their own rate and most are exceedingly rare. I've farmed Warrior maybe 20 times or more and only seen the Conference Call and Impaler once for example.

Sell value is pretty irrelevant in terms of quality. Certain things like rocket shooting Assault Rifles have extremely high prices but aren't particularly better. A white rocket AR sells for more than a purple anything else, generally speaking.