I'll try to make this brief...

Why can't a reduction in violence or more stability equally be termed a success?

Because if the surge doesn't contribute to long term stability in Iraq, as the lack of any hope of significant draw down indicates, than it is simply delaying the inevitable, and probably even higher; this is because by giving the Sunni militas breathing room from Shia death squads, they will be able to put up a greater fight in the future, thus causing more deaths. Unless you subscribe to the notions that future deaths are less important than current deaths, and accepting the notion that the surge hasn't made a long run contribution to Iraqi stability, then surge hasn't accomplished anything, and at the real cost of deploying those troops...

Of course reducing US troop levels is ultimately the goal, but why must this happen by July in order to call the surge a success?

Because that was the implication of the term 'surge' which the American public was lead to believe would happen. To toss this back at you, 'Why not 100 years? 200? It's all relative.' The answer is that the longer we are there the higher the real cost of keeping a garrison in Iraq (versus the speculated additional, indirect costs that MIGHT occur if we withdraw). There is no draw down in site, no firm date, and no reason to think it will happen anytime in the next decade. A boundless committment = failure, because commitments are costly.