EMB-545 flight crew reported receiving a GPWS alert during approach.

Narrative

At the beginning of the approach; aircraft experienced a flap failure. Missed approach was conducted and aircraft was vectored while checklist was completed.Twice; during maintaining this shallow glide path for the abnormal aircraft configuration; GPWS activated to alert the crew to terrain.Upon descending below the clouds during the second approach; and with visual of terrain and airport; aircraft; with gear down; was descended below the normal instrument and visual glide slopes so that proper final approach airspeed for the abnormal aircraft configuration could be maintained. In both instances aircraft descent was halted; while still having a visual of airport and terrain. Once GPWS alerts canceled; aircraft continued shallow descent while maintaining visual and appropriate airspeed. Aircraft landed safely without further alerts.In the conditions at the time; it was difficult to slow to the appropriate final approach speed for the abnormal aircraft configuration; however; it is possible a slightly steeper descent angle could have still maintained this airspeed; which may have resulted in no GPWS warnings.