Well, if everything worked normally for all those years, then the only reason why an outlet would start acting like it was on a switch - for no apparent reason can only mean that someone has done some electrical work. Maybe someone installed a new electrical outlet because the old one was getting worn out.
Important note of understanding: Every outlet has two sockets: one on top, one on the bottom.
My living room has four outlets, all of which are controlled by the light switch. Two of them I wanted both sockets to be on all the time, unaffected by the light switch. To do that I had to disconnect the wire that carried the current from the switch and jump the other wire back into the socket that was always on.
In my system, there are two hot wires, one black (always always always hot) and one red (on when the switch is on). The top socket WAS controlled by the switch, the bottom socket IS always on. Disconnecting the red wire and installing a jumper between the two hot screws on each socket (do not attempt to do this unless you are skilled enough to KNOW what you are doing - I'm not giving you ALL the details on how to do this) I made both sockets always hot, thus, both OUTLETS were made hot on one side of the living room while leaving the other two OUTLETS on the opposite side of the room to be controlled by the switch, the top sockets (each outlet) on the switch, the bottom sockets always on.
Your problem might be that the upper socket is controlled by the switch (or vice versa) while the bottom socket is always on. Did you move the plug recently? I mean, did you pull the plug out of the top socket and plug it back in in the bottom socket? (or vice versa)
If you continue to be unable to solve the problem with logic, perhaps a change to your circuitry might be an indication of another problem unseen, and seemingly not dangerous. I'd suggest having a professional look at the situation BEFORE you encounter an electrical shock OR fire.