I am so sorry to hear about Bertie. Thank you for requesting me. Sorry I was not online until now.
Since these little ones have small bones, they can break more easily. Did he have an accident, or fall, or was he just walking
around/normal activity when the bones broke?
Chihuahua bones do heal more slowly, and are more prone to "nonunions" (not healing) because they are so small. Often just putting on a splint or cast will not get the bones to heal.
I would be concerned that he could have some kind of problem that make the bones weaker, more brittle. Has he been getting puppy food, or what has he been eating? Is he getting any extra supplements or vitamins? (not recommended for puppies on puppy food since all the needed vitamins and minerals are in the food and adding extra vitamins and minerals can be harmful).
When he is xrayed, I would look to see if the bones look normal, or thinner than normal.
A bone biopsy might tell if the bones are normal or not.
Let me know what else I can help with or answer.