Is there a regulation that specifically states recovery periods for CQ and staff duty?

SSG (Join to see) Ft Knox, 1953. We pulled overnight guard duty and were returned to the company area in time for duty assignments. A Corporal commenced making protests that since we had been on overnight duty we were exempt from erecting the company’s tentage for an airing. The 1SG appeared, called the detail to attention and said, “erect those tents or I will charge y’all with mutiny”. Everyone slouched over to where the pallets of tents were. When I got tired of the detail’s pissing and moaning, I went over to a folded tent, grabbed a corner of a tent which didn’t move. I then called for assistance for that tent and all of the tents were erected within an hour or so!
One of my first acts of leadership!

There is under FM 22-6 Guard Duty an area for "Interior Guard" which could refer to Charge of Quarters .
CQ or charge of quarters is a tasked duty in which a United States armed forces service member is to guard the front entrance to the barracks. It is usually a 24-hour shift in which the two service members, one a non-commissioned officer (NCO) and the other a junior enlisted service member, sit at a desk to monitor incoming and outgoing traffic into the barracks. There are usually additional duties, such as sweeping the entryway, cleaning the entrance restrooms, and checking the barracks laundry room for laundry left overnight. Other duties may include performing radio checks every few hours with other company barracks and battalion headquarters around the base or surrounding installations as well as bed checks to ensure service members are in their rooms with their doors locked by curfew. For example, some U.S. Armed Forces service members stationed in South Korea have a curfew for being on post, and another one for being in their own individual rooms with their doors locked.
Weekend shifts USUALLY (but not always) start at 0700 hours (7:00 a.m.), depending on the military branch and installation, and go for 24 hours. During the work week, the duty starts at between 1600 and 1630 hours (4:00 p.m. and 4:30 p.m.), also known as Close of Business (COB). Service members are typically excused from duties the following day after being relieved by a senior NCO, in most cases the unit's first sergeant, though the CQ orders may say who in the soldier's COC may relieve him but at all times the unit 1SG will be apprised of the changes and receive his approval of changes.
However Unit SOPs vary between commanders and of course the mission of the unit dictates what the individual's duty will consist. A shift can be 2 hours on-shift 4 off-shit, 4 hours on-shift 8 off-shift, 8 hours on-shift 16 off-shift or even 12 to 24 shifts. When a soldier's relief is present a supervisor post the new shift.
The unit mission will dictate how long a soldier is given between duty off and duty on times.
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You did not give us a real lot information on the circumstances surrounding the incident.
Best thing is to do what your NCOs and other Supervisors say and use your COC to debate any problems about duty and time off.
Don't whine.

No actual regulation that I could find, hasn't been an issue for me though. Most commanders I've seen institute a policy if one isn't already in place. I've usually seen a 24 on 24 off before resuming normal duties. Watched a CSM chew out an SFC for putting a guy who had been on CQ for 24 on a driving mission, CSM told the SM he was excused and was not to perform any duties until first formation the next day.

So while there doesn't seem to be anything that covers it, it seems there's enough people in charge that know sleep deprivation has a negative impact on performance. Especially if vehicles or machinery is involved.

That said, there may be a regulation out there. No harm in asking, that's how you kill the BS that comes from PNN and NCO Chatter.