How many times can you reuse bones to make broth?
Beef bones can be used multiple times, but less flavor and gelatin will be extracted from each additional use. Harold McGee's "On Food and Cooking" describes this. 


  Because a standard kitchen extraction of eight hours releases only about 20% of the gelatin in beef bones, the bones may be extracted for a second time, for a total of up to 24 hours. The resulting liquid can then be used to start the next fresh extraction of meat and bones.


I would imagine chicken bones would be similar, although, since they are smaller, the first batch may be more effective than 20%.