LiteSpeed appears to have problems with all WordPress scheduled tasks that last more than a very short time – including all backup plugins. Adding this in an early position in the .htaccess file in your WordPress root folder may fix the problem:
RewriteRule .* - [E=noabort:1]
Adding the above line will make the LiteSpeed warning on UpdraftPlus’s settings page go away – this does not mean that the problem is definitely fixed; you will only know that via testing. If the above does not help, then you can try this: use WordPress’s alternative scheduling system – instructions here. The instructions amount to one thing: add a line to your wp-config.php file as follows:
If that does not help you, then you’ll need the help of your web hosting company to see why WordPress’s scheduler isn’t working on their setup, or is terminating it prematurely. Or failing that, you’ll need a different web hosting company. This problem is a generic one affecting all backup plugins on WordPress that run via the scheduler (which is all of them, as far as we know).