Fixing problem with contacts sync with google / gmail not working. Android.
Disclaimer: Nothing is guaranteed. Use this at your own risk.
If you manage to sync contacts just once (after deleting contacts storage), but never again, try to make some room on the phone (step 2).
Try in this order:Backup your contacts to sd card.
Then delete "Contacts storage".
Go to "Storage use" > All > Contacts Storage > Clear data
2. If 1 doesn't solve the problem ...
Make some room in the phone.
Your phone may say that you have 15+ MB free but it may fail to install a 0.7MB app (you can test it)
Make some room by deleting or moving apps to sd card. Then try to sync manually.
3.
If 1 and 2 don't work, delete all the updates on Google Store, and restart phone.
Hope it helps.