The Pleiades are 450 light years away. Thus when we see the twinkle in the night sky the light that hits our retina emanates from the year 1569 or so. On that proviso; how can we be sure that the star is still alive given the fact that we are seeing light from hundreds of years ago.
We don't know from sensory evidence. As far as we can tell, no information ever moves faster than the speed of light, so we are always at least 450 years out of date for anything happening in the Pleiades.
The only evidence we have is inferential: As far as we can tell (and we've looked real hard at this) the world works the same both here and at the Pleiades. And as far as we can tell (and, once again, we've looked real hard at this) stars like those in the Pleiades don't just disappear or go out in only 450 years -- it takes millions of years.
So, based on what we observe of them as of 450 years ago, and based on what we know of how stars work, we conclude that they are pretty much the same "today" -- though, really, what we're concluding is that when we observe them 450 years from now, they'll still look pretty much like they do today.
This is all inferential, but I'd bet just about anything on it. (If only I were here in 450 years to collect!)
We have a fairly good idea of how stars are born, how they evolve, and how they die. Numerical simulations allow us to the model the entire life of a star starting from its initial state (specified by mass and composition, mostly). Furthermore, we have various ways of determining the age of a star, and so we can therefore place it on a particular stellar evolutionary track and figure out where it goes from there. This means that we know if a star is likely to undergo some catastrophic transformation (say, a supernova) soon; if we don't observe it to be near the end of its life, we can be pretty sure that a relatively nearby star is still around (note also that 450 years is a tiny amount of time, even for the short lives of the most massive stars).
Age estimation is not an easy thing to do. There might be certain options available - comparing the target star to evolutionary simulations, measuring its magnetic field and rotation, etc. In most cases, not all of them are possible. Stars in clusters might be easier than field stars to date because the characteristics of the other stars in the cluster (e.g. place on a Herztsprung-Russell diagram) can tell us something about the age of the cluster itself, and thus of its constituents.
This is a boon for the Pleiades, and we have age estimates to within a factor of two. Observations of the amount of lithium in brown dwarfs (Basri et al. 1996) place it at $\sim$115 million years; comparisons to isochrones give $\sim$100 million years (Meynet et al. 1993), and earlier models gave values of $\sim$75 million years. That said, the stars in the cluster as a whole may not have formed precisely at the same time. Nonetheless, most of the stars in the cluster have lifetimes $\gg$100 million years, and we can therefore say with near certainty that they are still around.
...how can we be sure that the star is still alive given the fact that we are seeing light from hundreds of years ago.
The answers by Mark Olson and HDE 226868 both address the relative certainty that little will change in such a short (stellar) timeframe as 450 years. However, there's a deeper level that I thought deserves attention.
The fundamental nature of our Universe involves an information speed limit which is commonly referred to as the speed of light, with a value of exactly 299,792,458 metres per second. Our model of physics suggests that nothing can travel faster through spacetime than this, although expanding space, entanglement and hypothetical wormholes all make this more complicated than a mere paragraph can explain.
Nonetheless, a direct outcome of this information speed limit is that it doesn't really make sense to talk about "now" for any object at a distance. We can talk about that object as we currently observe it, and we can make predictions of what we expect it will be like when we observe it in the future (as the above answers have explained), but it makes no sense to treat it as though it's in the room next door. In reality, we live in an information bubble, where we can only ever observe objects in the past or events that have already happened. This is even true of the Sun: it was there eight minutes ago, but we can't say for certain it's there "now", we'll just have to wait another eight minutes to verify our extremely confident predictions.