Ideally you should use a sock to isolate the block from drafts. It will allow for a more stable temp.
You should also tune the PID in similar conditions to what you'd be printing in, so having some air flow from the fan is a good idea so that the tuning process gets a more accurate picture of what heat losses will be like during a print.
Also ensure that your heater cartridge is secured in the block and that the heat block isn't too far up and touching the heat sink. There should be a visible gap where the heat break is between the block and heat sink. If the block touches the heat sink directly it will lose too much heat to maintain a set temp.
Also verify that running M500 after the PID tuning actually saves the values to config-override. g and also that you have M501 at the end of your config.g to load those values at power on.