If something is proved to be possible, does that mean it can never, ever be proved to not be possible?

possible, practicable, feasible mean capable of being realized. possible implies that a thing may certainly exist or occur given the proper conditions

Proof of affirmative via experiment only proves "this particular thing did happen".  That has never been disproven.  The CONCLUSION that because this did happen then something else must ALWAYS happen is not proven.  A single case to the contrary disproves that extrapolation.

eg Galileo dropped a cannon ball from the leaning tower of Pisa.  It fell.  It is proven that it did actually fall on that particular occasion.

Now Galileo proposes that "whenever I drop a cannon ball it must fall".  That is a prediction.  If even a single time a cannon ball did NOT fall then we have disproven the claim/conclusion.  But NOT disproven the original experiment.

In science, nothing is ever proven. Math has proofs, not science. The reason is exactly what you said. A theory we thought was right could be falsified by future experiments. A theory in science might be accepted as the best we currently have, but it is never said to be proven. 

Back in the day. logic was taught in high school.  Now they don't even require it in college.  Go buy a book on logic and read it.  It will make hundreds of things much clearer for you  - even your question.   Let's start with the first sentence on Page 1:

                                 It is impossible to prove a negative.

I think you need to give an example because I suspect you are not expressing the question you actually want to ask. For instance, if you think Newton "proved" Classical Mechanics and then Einstein "proved" it was wrong, that is not really how a scientist would put it - then or now.

Let's start with the notion that science "proves" things are real, possible, whatever noun you want.  It doesn't.  The scientific method starts with a hypothesis - an idea that A results in B or a similar type of proposition - and then does experiments and observations to see if indeed the hypothesis is true.  But, the conclusion is limited by the range of the variables accessible to the experimenters and/or observers doing the experiment.  For instance, Newtonian mechanics works great for everyday applications.  But when you start to apply them to celestial motions (predicting positions of the sun, moon, planets, etc.), a discrepancy happens and the discrepancy is not explained by measurement accuracy or experimental error.  Namely Mercury has an "anomalous" precession of about 43 arcseconds in its orbit.  When Einstein developed the theory of gravity know as the General Theory of Relativity, he was able to predict the precession and also explain why it is there - something Newtonian physics can't do.  Does that make Newtonian mechanics wrong?  Technically yes but since those models work so well for speeds much less than that of light, and weak gravity (compared to that of a star), it makes sense to use them in day-to-day applications.  We say instead of Newtonian mechanics being wrong, that they are an incomplete theory.

There is also experimental errors that occur and in a rush to get out what appears to be groundbreaking results, gets overlooked.  For instance,  few years ago some researchers reported that they had measured neutrinos move at speeds faster than light.  There was a bit of press about it and the usual claims about hints of "new physics" but when outside scientists reviewed the instrumentation set up, they discovered a timing error and the "groundbreaking" results went away.

In short, we find new science by finding out where the established science stops working and then asking why.  SO yes - somethings are thought of as "true" but later on are either disproved (like the neutrinos) or are found to be approximations to a deeper theory (like Newtonian mechanics to general relativity).

You can certainly prove something is possible - simply by doing it.  That's not what science is about.

Scientific *theories* attempt to *explain* phenomena in the real world.  This is usually done by proposing a theory which can be tested experimentally.

A theory can never be 100% proven - only potentially disproven.

Scientists continually look for 'holes' in a theory in order to  improve (or replace) the theory.  For example, this may mean doing more accurate measurements (which become possible as technology improves) or measurements under more extreme conditions.

A real scientist would never claim their theory can not be improved or disproven.

show us an example of this...