Opt-Out, thank you for bringing this to our attention. Unfortunately, I have been unable to replicate the issue. I have a 4.5 GB test account with over 50,000 emails. In the web interface, I have been able to move varying number of messages (the most being 39,600 messages that I tried) between folders without message duplication, timing out, etc.
If the issue persists, you may consider opening a ticket with our support team. It could possibly be an issue with your client's mail account. If it is found that SM has a bug, your ticket will be refunded.