I have new Raspberry Pi 4. I am accessing it through SSH, ethernet cable to my laptop and VNC viewer to see the screen as I do not have spare screen. Whenever I try to update the Raspberry pi, it suddenly gets disconnected. When I saw the LAN cable connection on laptop, it showed that whenever I entered the command to update it, the LAN port on raspberry pi would turn off and soon turn on resulting in new IP address. So I have to again connect it to putty and VNC viewer. It's very frustrating. Currently I am using a 5V 3A mobile charger to power the Raspberry pi as I saw that people were suggesting that maybe the board would not get enough power to support components on it. In putty when I login it shows WiFi blocked by rfkill. The model I am using is Raspberry pi model B Rev 1.4
UPDATE 1- I tried one method mentioned in answer (to install screen first, then update), No results yet. The LAN port still switched off.
UPDATE 2- I bought official charger of raspberry pi and tried to power it. Still faced the same issue.
UPDATE 3 - I thought to see if there was any undervoltage due to power supply and ran the code "vcgencmd get_throttled". I got "throttled=0x0". On searching, I found that there was no undervoltage.