When I turn on my Yamaha RX-V657 without the speaker wire connected, it only stays on for one second and then turns off. No error is displayed on the screen. Is this normal?

Hey, if you find any difficulty then reset your speaker it might be helpfull for reseting use these steps::
1: Set the unit to Standby Mode using the Main Zone Power button.
2: While holding down the Straight on the front panel, press the Main Zone Power button.
3: When SP IMP -8ohms Min or SP IMP -6ohms Min comes up on the reciever panel, let go of the straight button.

Or for better guidance or more manuals click at manuals.plus:

1: Yamaha RX-V657

You forgot to see the AVR works prefectly using speakers
8,6 or 4 Ohms Z, selected to right ohms the switch.
does it? if yes he below is moot,

why do that.
it there is sound source running, and loud and you have no speakers there, that can damage some amps.
so don't do that, some AVR have no error code, protection lamp
just relay clicks
your AVR is really old a sea of RCA jacks on the rear.
there is no need to run any amp ever, lacking a set of speakers.
7.1, does have rules here, no sure me miniumum rules.
may be 2 are required min. (the selected set A or B)
what I do is read the manual first .
found it googled in 1second flat.
page 88

The protection circuitry has been
activated.
Make sure all speaker wire connections on this unit
and on all speakers are secure and that the wire for
each connection does not touch anything other than
its respective connection
Check that the impedance selector setting is correct
ok

I have repaired amps (AVR and others back to 1960s)
the protects circuits trip 1 or 3 ways or both (tech facts)

1. over currant the PA (power amps at speaker jacks)
2. or imbalanced driver transistor pair (push pull or class A)
3. or overvoltages there. now.