The problem of building a closed ecology is tough, but not insoluble in principle (though it probably would require rather more than a ton and a half of mass per person). Once that problem is solved, accelerating an "interstellar ark" to a speed that will get it to a nearby star before something critical gives out (i.e. a few percent of c) is also tough but not insoluble.
My favorite solution to the Fermi Paradox is the theory that, life inside the closed ecology becomes the "new normalcy" and that arks arriving at a new system just aren't all that interested in it except as a subject of scientific study and a source of raw materials (for the latter, asteroids and comets are easier than planets, if you're out in space to begin with). Thus, systems get visited but not colonized (at most, there would be the occasional long stop to build new arks when the old one gets too crowded or worn out).
I think it is insoluble, particularly if the fuel has to be carried by the ship.
My approach would be to reduce the material needs of the passengers to near zero (i.e., send intelligent robots).