BuddyPress.org

Are you taling about this cache https://wordpress.org/extend/plugins/wp-super-cache/ ?

bp does have built in support for this. If you can track down exactly when and where the avatars fail to load with it enabled it would help. Without being able to reproduce the problem in a specific area when this exact thing happnens or you do that thing, it’s impossible to track down the issues.

Try to reproduce the problem and post the results in trac as a bug.