and used the 'old bootloader' option as you suggested to upload my sketch while selecting the Nano board.
You will have to upgrade the board manager to version 1.6.21 (at the time of writing this, higher versions have a bug). You can use the 328P option once you have upgraded the board manager.
Board manager 1.6.21 will also give you the above mentioned 'old bootloader' option that you can use for older genuine Nanos and for clones.
but I would like to find out why this is happening. If you have any other ideas I would like to hear them.
The problem is that you have a genuine Nano that since the beginning of 2018 ships with a new boot loader.
I think you should use 328 with old bootloader and retry.