More to the point, a repeat offender reposting the same stolen stuff will almost certainly lose their hosting (assuming the host is responsive to DMCA notices).
Right, that's my hunch as well. If the complainant monitors the infringer's site after the first take-down, sees infringing content there again and sends a second notice to the host, the host would likely terminate the infringer's account -- or else risk liability itself. That said, I assume the onus is on the complainant to check the infringer's site from time to time. Right?
Perhaps I'm making too much of this. After all, who in their right mind would put infringing content back up on their site after its removal pursuant to a DMCA take-down notice? But then again, who in their right mind would intentionally misappropriate my intellectual property for profit, having constructive knowledge of the possible adverse consequences? (A rhetorical question, of course.)