Well, currently, unless something else kills you, cancer certainly will. Cancer is a biological inevitability, that can only be kept at bay for so long by the efforts of the human immune system. And as we all know, the longer we all live, the more of us will get cancer, because the transcription errors that eventually cause it become all the more likely as time goes by.
Bostrom seems to think -it's not expressed in so many words- that if we halt ageing, we'd also defeat cancer, somehow, perhaps by having an immune system that is forever as powerful as a young person's. The problem with this idea is that young people do get cancer, despite their healthy immune systems.
It looks like everyone alive has a probability to get cancer at some point in their life. For younger people this probability is relatively low, but currently, we only spend a few years of our lives (let's say 20) being young. If our "young" period is suddendly extended to 50 or 60 years, or more, the probabilty to get cancer while "young" in this sense, will increase. Imagine rolling a 100-sided die every year for 20 years, hoping not to roll a 01. Now imagine doing the same for 100 years. It's obvious that you're much more likely to roll at least one 01 in 100 years, than in 20.
So maybe Bostrom's magical health-extension pills won't work exactly like he thinks. Maybe we can all extend our life spans (well, those of us who can afford that mythical panacea) but not for as long as we'd like, and maybe we will find that if we extend our life for long enough, we will increase our likelihood to die of the most dreaded of diseases to an absolute certainty.
And wouldn't that really suck?