We present a comprehensive multifrequency study of the high-frequency-peaked BL Lac object 1ES 1959+650 using data from various facilities during the period 2016-2017, including X-ray data from AstroSat and Swift during the historically high X-ray flux state of the source observed until 2021 February. The unprecedented quality of X-ray data from high-cadence monitoring with AstroSat during 2016-2017 enables us to establish a detailed description of X-ray flares in 1ES 1959+650. The synchrotron peak shifts significantly between different flux states, in a manner consistent with a geometric (changing Doppler factor) interpretation. A time-dependent leptonic diffusive shock acceleration and radiation transfer model is used to reproduce the spectral energy distributions and X-ray light curves, to provide insight into the particle acceleration during the major activity periods observed in 2016 and 2017. The extensive data of Swift-XRT from 2015 December to 2021 February (exp. = 411.3 ks) reveals a positive correlation between flux and peak position.