I can see both sides here.
The thread title asks us: "Does Kevin Pietersen deserve the axe from the ODIs?" Well bloody oath he does! Absolutely. His performances have been terrible over an extended period and far below the standard a team of England's talent pool should expect. He's extremely lucky to be in the side and I find that a relatively easy question to answer.
The poll question asks us a very different question: "Should KP be axed from ODIs?" While he obviously deserves it, the selection of a team in any sport at any level isn't - or shouldn't, at least - be focused around rewarding and punishing players when they deserve it, but rather serving the best interests of the team in the short, medium and long terms. It's a far more complicated question to which I can see both sides. Obviously, yes, his performances have been terrible for quite some time, but I think the thing that saves him the most here is the fact that no-one really knows why, and hence we have comparatively little faith in the evidence of the last year or so as a gauge of what it is to come.
It's human nature to be more dismissive of patterns as coincidence when we can't grasp the causal link logically, and I think the fact that none of us can really pinpoint why Pietersen suddenly can't score any runs makes us all hesitant to suggest he shouldn't be playing. If he was getting to a typical age of decline, or had an obvious technical fault exposed, or had a poor domestic history in one day cricket that was finally catching up to him, or had an obvious life-changing personal issue that was clearly effecting his game, or even just looked really out of form at the crease, I think we'd all jump at the chance to blame it on that, drop him and sleep easily. None of that is really the case though - even though he's been pretty much the worst batsman in ODI cricket worldwide over the past couple of years, his previous performances at this level were so good for lunch a long time that his overall record is still amazing. The guy has proven he can play and that he belongs at this level. His domestic record in all forms is brilliant, he isn't getting out in any one particular way to suggest a technical fault (left arm spin jokes aside), he still looks relatively good at the crease most of the time before falling, he's still only 31 and nothing else has really changed at all. Combine all this with the fact that England have other more obvious problems in their team to address (Bell) and it becomes pretty murky. Personally, I'm pretty happy either way. He obviously deserves the axe but it may or may not be the right decision for any number of reasons; it's an impossibly tough call from my perspective.