This is kind of unclear to me, how do you create the files ? Is it >> (append) or > (redirect), what format is that ? What is the OS ? How are you sure what's happening with the connections ? What if they got closed for some reason ? Given the conditions you've posted, Connection A will be the same in the second file, but tcpdump will eavesdrop the current flow, i.e. timestamp will be different.
Please post more details, as well as log snippets, if possible, so we can answer this correctly, in case I got it wrong.