Are you powering your RPI 3 via GPIO or via microUSB? And did you measure the 5.2V under load or when the PSU is idle?
The microUSB specifications list a amperage of maximum 1.8A for this type of connector. In general the microUSB socket/plug isn't that great when higher power is demanded because they have tiny connectors and a quite high resistance. They also tend to degrade quite quickly and a loosy connection is often what I got with my microUSB sockets/plugs.
Still testing another PSU might be worth. I have 12/24V PSU which worked for years for long runs of led lightning and one day started to produce a more or less regular flicker. These PSU still have the rated voltage (even under load) when measured and "look" fine but I degraded them to simply open and close valves now because they are not fit for my lightning applications anymore. Maybe some capacitors lost some liquid and the ripple got bigger? Power supplies age - and mostly they don't age well.