Not sure if this has anything to do with it as I don't know whether you are using a drum editor and I think this usually applies to the end of songs BUT if you are using something like BFD for drums be sure to set the sequencer to Offline otherwise notes and tails can get cut off when bouncing.
If this is just audio maybe drag out the start of your clips so there is a lead in before the audio starts. This might fix it because the computer is already mixing down by the time the first transient hits. Then trim it after the fact in a new project or in something like Pyro.
Also try disabling Fast Bounce in the Export options. That can sometimes make things go wonky.