Have the same problem. AMPPS-3.8 32 bit works fine on Mac OS Mojave 10.14.5.
And before upgrading my system to Catalina I want to install the 64-bit version (cause it only supports 64-bit apps). I renamed my current /Applications/AMPPS to /Applications/AMPPS32 and installed AMPPS-3.9-x86_64.
A strange authorization dialog popped up. And new AMPPS rejected my name/password