48 hours is the time require for action I believe, however the claimee can respond in however long they like, but the content must be unavailable until they file a counter claim.
72 hours to take down the infringing content upon receiving a valid DMCA notice. The content owner gets notified and they can then file a valid counter-notice. Then the counter-notice gets filed with the copyright claimer and a 10-day waiting period starts. If the claimer does not file a counter-counter-notice within the 10-day waiting period the content gets reposted. If they do file a counter-counter-notice, the ball gets passed back to the content owner to file a counter-counter-counter-notice and the 10-day period and claim process starts over.
As someone who runs a site that hosts content, this is great for us. We aren't allowed any sort of leeway in interpreting the claims and in return we are exposed to no liability. We are simply the middle man and have to do what's asked of us.
So the hoster doesn't actually need to take the content down right away, but within 72 hours? That is, if the customer files the DMCA challenge within 72h, then the content will have always remained up? My questions here are with regard to continuity of availability.
(IANAL)