Power-button never shut off a PRS-505. It will just set it into standby.
Anyway, after one hour idle, the PR-505 will enter standby automatically.
As restarting or a soft-reset (press the reset-button with a paper-clip) didn't solve your problem there might be a hardware issue with the power-switch.
You can try to install PRS+.
PRS+ allows to assign any button to put the reader into standby, and it allows to set the auto-standby time to a shorter value. Like 5 minutes.
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