Hi, 

It is likely losing leaves due to the change in environment and humidity but it could also be going dormant for a period. I also had a type of Rex Begonia do this and recover, and then ultimately perish when it got too dry while on vacation one summer. I'm not sure why it didn't go dormant last year, but maybe the move inside didn't shock it as much.

Make sure it doesn't stay too wet, but also don't let it dry out completely. When the first inch or so of soil is dry, water again. Bottom watering is helpful since they are shallow-rooted. This allows the roots not to sit in too much water. If you haven't repotted and it's getting root-bound, wait until the spring to do so. 

The New York Botanic Garden has a comprehensive webpage on Rex Begonia care. Check out the section on Dormancy, which we linked to directly. 

Let us know if you have further questions. 

Emily