The price was kept very close to a dollar on trading exchanges (within 2-3%, often within 1%) for a few months up until just before the last hard fork, which also happened to be the time that Tether (another dollar-pegged cryptocurrency) started having problems. It is difficult to pinpoint the exact causes of the difficulties but it seems that SBD can keep a peg under some conditions but not others. To make the peg more reliable something needs to be improved in the mechanism (even if it does manage to recover on its own and sometimes works as-is).