Hi Amber,
It looks like your Begonia has weakened roots from previous lack of good care. Sometimes
plants with seriously compromised roots will hang in there for a long time before eventually dying. Sometimes they will gradually reestablish themselves and the
plant will respond accordingly.
Make sure your Begonia gets lots of sun. Be very careful about the watering because there is little margin for error with those roots. Remember to keep the soil drier than normal because the roots are not using much water.
It looks like there may be some fungus near the base of a couple of the stems, although that may just be light reflecting in the photo. Begonias are very susceptible to fungus.