We present the results of a search for long-duration gravitational-wave transients in the data from the Advanced LIGO second observation run; we search for gravitational-wave transients of 2 -- 500~s duration in the 24−2048\,Hz frequency band with minimal assumptions about signal properties such as waveform morphologies, polarization, sky location or time of occurrence. Targeted signal models include fallback accretion onto neutron stars, broadband chirps from innermost stable circular orbit waves around rotating black holes, eccentric inspiral-merger-ringdown compact binary coalescence waveforms, and other models. The second observation run totals about \otwoduration~days of coincident data between November 2016 and August 2017. We find no significant events within the parameter space that we searched, apart from the already-reported binary neutron star merger GW170817. We thus report sensitivity limits on the root-sum-square strain amplitude hrss at 50% efficiency. These sensitivity estimates are an improvement relative to the first observing run and also done with an enlarged set of gravitational-wave transient waveforms. Overall, the best search sensitivity is h50%rss=2.7×10−22~Hz−1/2 for a millisecond magnetar model. For eccentric compact binary coalescence signals, the search sensitivity reaches h50%rss=9.6×10−22~Hz−1/2.