Had a quick search of the forum but couldn't see any posts re this... I know it says "must" on the Minor Essence Drain card, but can you choose not to pay the mana for the creature and let it die? Or do you have to keep it alive if at all possible by paying?
Interesting question - this never occured to me as I always interpreted this along the lines of the "upkeep +X" trait in Mage Wars Arena. So to me personally it is interpreted as you have to pay or else your creature dies i.e. you have the choice. Having said that my interpretation may be wrong as minor essence drain does not have upkeep+1 but uses a different text.