Hello This is verry strange problem personaly never have that one. Try to share the problem in Face book groop Anet A8 3D Printing it is have a lot of members that sharing different problems. And If you Cura user chesk you settings for zero positioning starting or something like this it must be unchecked.
I did got the problem with my printer as well. I used Cura and tried to mix something up in the Extensions -> post processing -> modify g-code. While adding the script "change AtZ..." or "filament change" (I cant remember correctly), the phenomena is exactly like what you describe. After I removed the script, everything work normally. Maybe you should check this option. Sorry for my bad English.