I too have this problem.
I use the default template on one website, and here's where this problem occurs.
I have a couple of other websites on the same shared server, PS 1.6.14, php 5.3 and 5.5, mysql 5.5 and MariaDB, these work fine. Slow, but are working, can add products.
The "Save and Save & Stay buttons on the website with the default theme just keep spinning and spinning, no matter how long I wait.
The other tabs are completely blank.
I have tried a few of the suggestions here, comment out mod_evasive, remove diabled from /controllers/products....no luck.
I have contacted my hosting company, but they are stumped as well.
I really hope this is solved soon.
It seems that there are a number of different solutions, no one standard.
Cheers
Endre