Looks like the default for DietPi in /etc/php/7.0/fpm/pool.d/www.conf for pm.max_children is 1.
This caused a problem for me when I tried to use FreshRSS together with RSS-Bridge, hosting both web applications on my Raspberry Pi, and I suspect it would cause problems with any other web applications that make requests to other local web applications. It made it impossible for me to add feeds from RSS-bridge into FreshRSS.
I set pm.max_children = 4 and rebooted, and now it works fine.