XPS 13 9300, Ubuntu 20.04, deep suspend not working

I have observed an issue with the Dell XPS 13 9300 where it cannot enter deep sleep. As a result, the battery runs down very quickly when you shut the lid. The machine originally came with Ubuntu 18.04, which has the same problem. I thought upgrading to 20.04 might help, but the issue persists.

I can tell the machine is entering s2idle instead of "deep" suspend by running the steps here. And here.

As per this thread, I tried disabling "signs of life" in the BIOS but that did not help.

The steps taken were:

- Make sure I have the latest BIOS.

- Disable "signs of life" in BIOS.

- Run "echo deep > /sys/power/mem_sleep" 

- Verify that this setting took effect.

- Then run "systemctl suspend"

No dice - the laptop cannot wake up and needs to be restarted. Anything else I can try? It's a frustrating issue since the machine must be powered off when closed.