The International Astronomical Union (IAU) defines planets by three criteria:
- "is in orbit around the sun"
- "has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape"
- "has cleared the neighbourhood around its orbit"
The last criterion seems to cause some confusion, but it is mean to imply "[the body] has become gravitationally dominant, and there are no other bodies of comparable size other than its natural satellites or those otherwise under its gravitational influence." This is where Pluto fails on multiple counts as it is "constrained in its orbit by the gravity of Neptune and shares its orbital neighbourhood with Kuiper belt objects."
If we assume that a solar system body being studied is easily determined to be "nearly round" then all contention will center around the third criterion. If a planet is declared, and then "demoted" to dwarf planet because it is found not to have cleared its neighborhood, I can think of two ways it would be deemed a planet again in the future:
The neighborhood becomes cleared. This is incredibly unlikely, but consider the case where two massive bodies share an orbit - possibly in stable equilibrium. The loss of one body (say due to large gravitational influence of a passing object) would leave the remaining body in a "cleared" neighborhood and thus it would be reclassified to a planet. I cannot stress how improbable this is, but I can't prove it couldn't happen so I will assume it may be possible. For Pluto, however, this is essentially an impossibility. Any event that somehow cleared the Kuiper belt of objects would almost certainly affect Pluto as it is itself a Kuiper belt object. If some event were to destroy or move Neptune (somehow without affecting Pluto), Pluto would still remain in the uncleared Kuiper belt.
The classification system changes. The system is essentially just semantics that are agreed upon by a single governing body. For instance, people in the field of planetary science tend to refer to moons, asteroids, dwarf planets, and Kuiper belt objects in the solar system without really invoking the planet/dwarf planet distinction. They all know the eight most massive bodies, and they know quite a few smaller ones as well, and their research isn't really based on how these bodies are classified by the IAU. In much the same way, the classification system could change and the solar system would keep on turning.
EDIT (to answer more precisely about when and how this could happen):
To clarify, the insistence that 1. is an unlikely scenario is based on the fact that a situation such as I describe above is unlikely to occur at present in the established solar system. The only scenario that comes to mind in the current solar system is the case where a planetary moon is ejected and finds its way into a stable orbit (again, the likelihood is low but it is possible under the right conditions). As our moon moves slowly away from the Earth, it is theorized that it may one day escape the Earth's gravitational influence entirely (of course, the opposite is theorized as well). If it were to escape and find its way to a stable orbit, it would become the largest dwarf planet in the solar system.
However, in the case of a newly forming solar system, an observer would most likely observe planets being demoted to dwarf planet and then later reestablished as a planet. In such a case, an existing planet could find a large body of comparable mass kicked into its orbit. For as long as the orbit was shared, both objects would be dwarf planets. The same planet could also find itself a new member of a co-orbiting system where another large body has become quite close (think of the situation if the moon was considerably larger). Then as before, it would be demoted to dwarf planet. These situations are inherently unstable: in the former case the new object would be kicked into another orbit or collide with the original planet, and in the latter case the two objects would almost certainly collide (maybe forming one big planet or a planet-moon sytem). The instability in these situations is what makes a planet->dwarf planet->planet change in status unlikely at present. All/most of the unstable conditions of the early solar system have since settled into equilibrium.