Make sure description and short description have no HTML codes and try to save. It should work.
that's right @SultanRana ,
many times could happen there is just a mandatory field not filled up.
i.e. if you delete a manufacturer then try to edit a product that had that manufacturer, the button save won't work: you must scroll down to see the error in the "manufacturer" field.
that could be tricky because the user expects the error to appear on top of the page too, as usually happens with html5 forms.
anyway, hope that could help people troubleshoot the issue in the most simple way before trying to redeploy or edit the code
Scroll down to attributes section in product page and see if you didnt fill value for mandatory attributes.
Make sure to check "Advanced Pricing" visible after clicking the link under Price, if all other attributes seem populated.
Check your advanced inventory information / Maximum Qty Allowed in Shopping Cart
This field must be either empty, or have a value greater than 0.
another option is to tick the checkbox "Use Config Settings", and make sure the configuration is set correctly.
I got this issue, I wrote a post here for this. Hope this helpl