It should not, and this is worth understanding because it separates a robust migration from a fragile one.
Aggressive idle timeouts are normal on shared hosting. A migration that treats a dropped connection as a fatal error will fail constantly on these hosts. The correct behavior is to catch the disconnect, reconnect, and resume from the last confirmed item — not restart the folder from the beginning.
Because every item is tracked individually and matched by a content fingerprint, resuming after a drop does not re-copy what already transferred and does not create duplicates. In practice you will see the transfer pause for a few seconds and continue. You do not need to babysit it.