Laptop sometimes shuts down when out of power causing me to lose my unsaved files

You should not be letting your battery get to 0% - at minimum its killing what battery life you have left.

It sounds to me that your battery is well past its useby date, and may simply not have enough juice left in it to reliably shut down the system when it runs out of power - if it can't finish suspending then of-course its going to shut down suddenly and you will likely loose unsaved work.