breakpoints are currently not tracked as part of the task context. The focusing in the breakpoints view shows breakpoints that are related to files that are part of your context only but does automatically manage them.
Your suggestion sounds very interesting and there is a related discussion in the Mylyn bug tracker to add this functionality:
155333: Include breakpoints from the current context into the context data
Please feel free to add your thoughts to the Bugzilla report and vote for it!
Committer, SpringSource Tool Suite
Senior Developer, Tasktop