The obvious upper bound on "forever" is the useful life of the universe (i.e. enough negentropy is left to support life). More realistically, no pill will prevent your body from being horribly mangled in an accident and very low risks for accidents pile up to probability 1 over long enough times.
Even then, there will be a small chance of something happening that kills you and destroys all of your backups. Over a long enough time span, the probability of that happening approaches 100%. You could make it a very long time by doing that, but not forever.
Because the universe will end at some point, either getting to a point of maximal entropy, or via a big crunch, or some other unknown mechanism.
One could conceivably escape from this by escaping to another universe - if that's possible - but that's just fantasy at this point. As far as we can tell, even if you can live basically forever you will eventually cease to exist, when the universe ceases to be an environment that's conducive to existence.
So it's physically impossible to live forever. A few hundred billion years is probably an upper bound. Not a shabby run, but not forever.
We can "slow down" the "speed" of time using virtual worlds. Also we can split personalities to have many experiences in the same time. That is providing physical laws cannot be altered in the first place. I think galaxy-wide strong AIs will have better ideas then me, so consider the entropy problem solved.