I too am experiencing persist ‘HTTP error.’ messages while uploading media to a 4.3.1 site.
I have tried:
1. Deactivating aps
2. Changing theme to 2015
3. Reinstalling WP 4.3.1
4. Re-setting plug-ins via FTP
5. Looking at wp-config (not sure, but it looks OK)
6. Looking at htaccess (not sure, but it looks OK)
Any advice would be really appreciated.