I keep clicking the button everytime the window pops up.
How often this windows pops up depends on the number of rows in the statistic database table of your blog. It also depends on the increment you choose. If you don't change it, it will always be the default value 10. If you db table has for instance 100000 rows then you would need to restart the upgrade procedure very often (in this example: 10000 times).
If the execution time limit is bigger than 10 seconds then you should have a look what the possible increment is and increase the increment to the maximum.
What worries me, is that you have quoted the displayed text with the placeholders "..." instead of with numeric value. Doesn't the time value and the number of the upgraded rows change after each click on the button? Are the points always there?
Furthermore it seems unusual that the max. execution time would change from time to time.
It would also be helpful if you could try to find out the max. execution time limit with the help of a different plugin. There are many system information plugins in the repository. WP System Health is the one I usually use for such purposes.
If you use this plugin then you should be able to find the values at the plugins page: open the PHP panel and display the Core information. The
max_exectuion_time values should be in this section.