Electronic – Resetting CD4017 Counter when power source is OFF

My bet is on boot0; Check that you've got it pulled low.

The boot0 pin selects where the MCU will start executing code from when it boots up, ie. comes out of reset. If boot0 is low, it'll execute your code from flash, but if it's high, it'll execute the internal bootloader from the system memory.

My guess is that you have left boot0 floating, and when you're doing a cold boot (ie. disconnecting and reconnecting power), it'll be close to zero, so the MCU will boot your code from flash, but when you do a warm boot with the reset signal, the pin will have floated to a higher value, is read as high, and the MCU will boot to the internal bootloader from system memory instead of your code.

This explanation assumes you haven't touched the boot-related option bytes, which would change the behaviour. Also, in case you'll be working with different STM32 MCUs at some point, please note that they can have slightly different behaviour. Some have different boot-related option bytes. All I've seen so far have had a boot0 pin which behaves identically, but some also have a boot1 pin (which might be shared with a gpio pin) that you might also have to set correctly. In the MCUs I remember seeing, though, boot1 is only relevant if you want to be able to boot from system memory or SRAM.

The 4017 is clocked on the rising edge, and you have the clock line high when it comes out of reset.

Try connecting clock in to Vdd and the 555 output to inhibit in. Inhibit is just an inverted clock input (sans Schmitt trigger). Or add an inverter between 555 and clock in.

In general this is a really crummy reset circuit - criminally bad for anything important. Use a reset (supervisor) chip that provides a sharp fixed-length reset pulse out (eg. 200ms) and also detects slow brownouts and slow Vdd rise. They are plentiful and cheap, and designing one that is bulletproof is non-trivial.

If you insist on using this circuit, at least add a few K resistor in series with the reset input. Otherwise shorting or putting a heavy load turning Vdd off could damage the chip by discharging the 4.7uF through the input protection diodes.

Edit: Rough schematic showing supervisor chip ADM803/ADX803, you may want to add a power-on LED or resistor from Vdd to GND to help discharge the 5V faster so it resets reliably on a short power interruption.