Is the time for the Extreme Survival milestones cumulative?

Once you leave the planet, the timer resets.

You can stay inside a shelter and the counter will continue to increase. But I believe you have to be on an extreme planet, not stay out in extreme weather. The easiest (though most tedious) way to get these milestones is to just hang out in a shelter doing nothing.

A sol seems to be about 15 minutes.

This has been fixed as of version 1.07. Progress towards the Extreme Survival milestone is now cumulative.

From the patch notes:

Some players were unable to achieve the extreme survival journey milestone, this has been resolved.

This post clarifies what that means:

The issue where the counter would reset when leaving the planet's atmosphere was fixed.

If your save is from a previous version of the game, however, then your counter will already be 0, and you'll need to build back up to your previous total before you'll see progress in the milestone menu (since it's now incremental, you can do this over time by visiting a number of extreme planets).