The nature of feudalism
Feudalism is probably best described as fractally distributed authoritarianism. It means that political power is (theoretically) organized as a tree structure, with obligations of fealty that go up the tree (and sometimes down; European feudalism had formal recognition of bidirectional obligations, while the samurai of medieval Japan conceptualized their loyalty to their lord as one-way and absolute.)
This means that any subset of the political structure is potentially autonomous. Let's say, and why not, that you are a medieval European Baron, and you owe feudal duty to a King. What happens when the King dies without an heir? Well, you pretty much keep going: running your barony, intriguing against your neighbors, keeping the Vikings or whomever at bay as best you can. At some point, you will be offered opportunities to swear fealty to some kind of suzerain; you may even take part in the intrigues attendant on creating a successor's claim to the throne...
The point, of course, is that the death or loss of legitimacy on the part of a leader does not cause as much widespread ruin. The system reconfigures itself, more or less naturally. This creates a very stable political situation. Probably the most stable that could be contrived, given the tumultuous nature of medieval times.
That resilience is the core benefit of feudalism.
Where it comes apart, historically, is when a society starts generating enough economic surplus, or encounters sufficiently uncharted circumstances, that feudal suppression of the peasant base becomes insufficient as a political model. I've recently heard Democracy described as "the crowdsourcing of political decisionmaking", and I don't think that's entirely wrong.
A secondary downfall of the feudal model would be when economic and technological factors make it impossible for the nobility to sustain its position. This is often characterized in historical recapitulation as "when central governments got cannon and could reduce castles at will". That, however, is an historical artifact of European history. Your question isn't about that.
Would it be possible for a sufficiently powerful (politically and technologically) 'elite' class to oppress the masses and re-enforce a feudal style society?
The best answer I can give you is another question:
Can your envisioned high-tech society provide a set of circumstances in which:
- extending power to the common people is not necessary, and
- the independence of a "nobility" can be expected?
If you can answer "yes" to that question, then you have a plausible scenario for the existence of a feudal political system. For this, you will need to tweak your technology, and probably your planetology, to make that happen.
To go beyond "a plausible scenario", however, you need to find a situation in which the nested resilience characteristic of feudalism is not merely conceivable, but confers a strong advantage.
Some factors that could work toward this include:
Geographical boundaries that are not easy or cheap, even with your postulated high tech, to traverse with military force.
Interruptions to long-range communications (perhaps due to peculiar characteristics of the sun's radiation, for example?)
Cohabitation on the planet with formidable and unpredictable competitors.
Intense bombardment by meteors at difficult-to-predict intervals.
The existence of destabilizingly strong and destructive Wild Talents (psionic, or even more radical) amongst the population, including the "common folk".
The existence of high-tech power generation systems that have a strong tendency to become unstable if you build them too large. Sort of the equivalent of a nuclear explosion, sometimes... This would cause an enforced decentralization of energy resources. Decentralized power is much the same thing as decentralized productive agricultural land in medieval feudalism...
These are only a few ideas that would tend to make feudalism a better choice than large-scale authoritarianism.