I can't see this being a memory leak problem with the server. If that were that case then this forum would be full of posts about it. It doesn't appear to be related to file size either as I can quite happily copy 5GB+ files with no problem.
So it must be something to do with the app. The only thing that comes to mind is if the app is trying to do lots (10+) of concurrent file transfers. I would speculate that in that circumstance the router might run out of memory or become unresponsive.
Thanks for your reply. I think you got a good point here. Perhaps Merlin could confirm this. Is there a way to capture Samba logs during sync?