A lot of web hosts limit the max execution time of scripts running on their service and the Inventory sync module hits way over most of those limits of around 180 seconds.
Is it possible to change the module to sync the selected products in small batches so it would work in any hosting environment? For example if you were syncing 100 products the script would split the products into 10 groups of 10 to sync so each script would stay under the max execution time. A feature that could be enabled would be sequential or simultaneous sync. Simultaneous would kick off all groups at once and sync the products faster but use more memory and sequential would process the groups one at a time to reduce resource usage.