Are enemy drops affected by player death?

I've been wondering if the loot dropped by a boss/sub-boss/badass is affected by you dying before killing it?

I'm wondering because my boss-loot is usually pretty crappy, most of my unique/legendary items having been box-drops.

No it doesn't affect it in any way. Minor loot (money, ammo) eventually disapears after so much other loot has appeared or if you've left the area, but dying doesn't downgrade loot, whether you die before or after beating the boss. Nothing changes when you die except you lose money and all live enemies have their health reset to max (In coop, all players in an area have to die for health to reset).

Also note that boss-drop rate for legendary/orange items is like 1% in Borderlands 2. And that's from the boss that drops the item; it's far lower for all other bosses/chests. Unique (blue rarity + red flavor text) guns are usually fairly common drops but only drop from a single specific boss. You're probably not getting significantly worse loot than anyone else.

Also note that dropped items or rarity green any up will stay in an area even after you've left (for a time). It seems the rarer the item the longer it persists, but if you quit the game it's all gone of course..

No it's not, if you stay in the same area without reseting the game or leaving the area, the loots stay there and no change are made on their stats.