The problem with being Mr. Dependable is that you run the risk of turning into the ubiquitous punching-bag or consummate pin-cushion.
The more that you offer yourself to a broken system, the more that system exerts an increasing amount of control over you. Staying up late, working on something well past the window in which you would have been effective, not being provided the help that you need to complete a project or fix a problem–these are all things that fall squarely in the “Not My Problem” category.
The trick is finding the balance between the two poles and evaluating the situation for yourself. Abandoning ship only makes sense when you’re able to make a cogent argument for your health or your sanity… or if the ship is poorly-built to begin with.