If you are using XAMPP or WAMPserver on Windows you might find that your archive extraction suddenly stops. Unfortunately, this is a bug in how XAMPP and WAMPserver are set up. Their developers are using the non-thread-safe version of PHP as an Apache module. Unfortunately, Apache requires thread safe (ZTS) builds of PHP or it will corrupt its memory, killing the PHP process. This happens when there are numerous requests in quick succession such as when building a complex site, taking a backup or restoring a backup archive. The same thing happens when you try to restore a large database (SQL) file with phpMyAdmin using the automatic continue method.
Please note that we DO NOT have any control over this. If anything, these people should know better than to ship XAMPP and WAMPserver broken like that on account of this information being printed on the PHP download page for Windows on the official PHP site.
There are two things you can possibly do.
The best solution is to use a different local server. You can use MAMP Pro or build your own server using Windows 10's IIS, MySQL and PHP. Understandably this is not the easiest solution.
As a compromise, you can try to change the time settings of Akeeba Kickstart at the bottom of its first page and before clicking on the Start button. Recommended values are a Maximum execution time of 10 seconds and a Minimum Execution Time of 20 seconds. Yes, the minimum is higher than the maximum to allow for a "dead time" which allows Apache to spin down previous PHP processes, avoiding the pitfalls of using the non-threaded version of PHP as a module.
Again, this situation is beyond our control and there's not much else we can do about it. Please ask the developers of XAMPP and WAMPserver to fix their software.