It may be too late this season but it depends on where you live. It sounds like they may not be getting enough light and fertilizer or possibly too wet. If you have to bring them indoors for winter, then next season gradually move them to a sunnier location so they can toughen up and feed on a regular basis. The other suggestion is to have them under a roof so rain won't break any stems.

You may also cut them back heavily, to near a few inches, and allow them to regrow stronger in better light. These begonias prefer strong light, to dry out considerably, and will grow all year if light levels are good. Always keep them dry after pruning until growth resumes! Greg Sytch ABS Horticultural Correspondent