Well lets see here, where to begin...
First, the odds of a society advancing to the future tech, system spanning empire you mention, having ALWAYS been a feudal kingdom is completely impossible.
As a general rule feudal systems don't do much to promote long term technological and economic growth.
Traditionally feudal systems existed to keep the rich and powerful well..rich and powerful. Changing your status was virtually impossible and the common folk were generally viewed as a common resource like wood and stone.
If you think wealth concentration is bad in the modern era...well lets just say the middle ages were way way worse.
Education also tended to not be important or supported outside the ruling elite, its tough to maintain power when you have an educated populace, there is a reason that dictators tend to either exile or murder intelligent people when they come to power.
The main point here is: Your empire didn't start a feudal system and remain that way from the Medieval era to the far future era.
With that point settled the question remains, how could a system spanning empire with a true feudal flavor exist in a far future setting?
Well...its impractical as feudal systems tend to be more and more inferior in efficiency the larger they grow in size, that said, we can probably set up a plausible or at least acceptable scenario to get there, after all, there are still plenty of monarchies today even when to most of the world they make no sense.
Reasons for a monarchy rising in a far future setting:
Unrest/War: If things get bad enough, and a strong man steps up and makes things better, the people are still people and security is very important to them, no matter how far in the future.
Apathy of the citizenry: If the people are happy...they may just not care. That family has been in charge for 200 years but I have my space big mac (TM) and my space smart phone (TM) and my space...whatever (TM) so I just don't care.
Being Sneaky. In a lot of cases we see what is in reality a monarchy arise without the label. Usually this is done through manipulation of the legal system. This will require a massively popular (Hugo Chavez for example) leader figure that the people like enough to give up political freedoms etc.
Super wealth: Middle Eastern monarchies are probably the best modern example of this, and it overlaps in may ways with the apathy option...if the government gives you lots of money due to having a much desired resource, you probably don't care who's in charge as long as they don't interfere too much with daily life.
Odds are it ends up being a combination of the options I listed, or even the myriad of other options I did not list out.
I should also mention I love the idea of a space armada where the king is in a gargantuan capital ship, the Dukes are in cruisers, the Barons in Carriers, and the knights fly around in large interceptors. Meanwhile the grunts are stuck flying in fighters...each unit has their boss' coat of arms painted on their craft...very cool mental image.