We present an analysis of data from multi-frequency monitoring of the blazar 3C 454.3 in 2010-2012, when the source experienced an unusually prolonged flare with a duration of about two years. This corresponds to the orbital period of the companion in a scenario in which two supermassive black holes are present in the nucleus of 3C 454.3. The flare's shape, duration, and amplitude can be explained as a result of precession, if the plane of the accretion disk and the orbital plane of the binary are coincident. We detected small-scale structure of the flare, on time scales of no more than a month. These features probably correspond to inhomogeneities in the accretion disk and surrounding regions, with sizes of the order of 10(15) cm. We estimated the size of the accretion disk based on the dynamical and geometrical parameters of this binary system: its diameter is comparable to the size of the orbit of the supermassive binary black hole, and its thickness does not exceed the gravitational radius of the central black hole. The presence of characteristic small-scale features during the flare makes it possible to estimate the relative time delays of variations in different spectral ranges: from gamma-ray to millimeter wavelengths.