I don't have a solution then. If the avi files play correctly on the hard drive, they should transfer properly to the BD-RE dics.
Did you burn with ImgBurn? I recommend that program for all burns to blu ray media.
Did you test playback immediately after burning? Or did this problem occur much later?
What type of BD-RE dics are you using? I don't have much experience with them other than a few Japanese made dics that were briefly sold under the TDK brand. The Japanese made media from that time was excellent and my discs have held up well.