The"Runs fine for 20m"part worries me. Sounds like that circuit is holding a load long enough that the constant current might be heating something up and then a connection is going bad. Then once it cools, you have a connection again. If something was tripping it might be easier to troubleshoot the circuit. Personally, first I would trace your circuit out, and I would try to see if the hallways plug is on the same circuit (newer homes it won't be, but you never know depending on the electricians or house age). If it is on the same circuit, then you can probably eliminate there being a problem in the panel. If it isn't on the same circuit, I'd then wonder if your circuit feeds only that laundry room (newer code) or if it's tied to other stuff. If it is tied to other receptacles, you could get the cord back out and try running off those - sometimes you can isolate a fault that way.
I imagine I would end up looking at your breaker (busbar tabs and wire terminal) and then every single connection made in that circuit inside junction boxes. I cannot tell you how many times I've pulled receptacles out and seen problems that you can't see otherwise. The push-in connections are a common issue, as are bad splices (sometime you'll have one wire in a wirenut not actually IN the inner coil, but the twist of the wire is keeping it 'kinda' secure).
If it isn't a connection/splice somewhere (or that duplex receptacle is on a dedicated circuit) and everything else looks fine, I'd think about swapping breakers. So, if that's a 20A, find another 20A circuit/breaker and just land Circuit A on Breaker B and Circuit B on Breaker A. If that holds, then there is something wrong with the breaker.
An intermittent problem like that can be a real PITA for electricians to find w/o having to keep waiting for 20m. I guess that's why I would first trace the circuit out and then go looking at connections, instead of trying to isolate the breaker or trying to split a circuit into parts to test. A dead short is easy by comparison. Since you're the homeowner though, you can try things like swapping the breaker out first and waiting 20m w/o having to worry about doing that as an electrician. I'd hate to come to someone's house, swap the breaker, wait 20m and then find out that the breaker isn't even the problem, LOL.