I have the same problem. If the Emacs app is not open, and I drag a file onto it, it opens. But if I drag a second file onto the Emacs app when it is already open, nothing happens.
This happens on both version 26.3 (the latest release available from
emacsformacosx.com) as well as the latest nightly version, 2019-10-21, from
emacsformacosx.com.
I see the following line in Console when I try to open the second file:
LaunchedApplication: failed with error -13052 (null){ "ApplicationType"="Foreground", "BundleIdentifierLowerCase"="org.gnu.emacs", "CFBundleExecutablePath"="/Applications/Emacs.app/Contents/MacOS/Emacs", "CFBundleExecutablePathDeviceID"=16777220, "CFBundleExecutablePathINode"=39467615, "CFBundleIdentifier"="org.gnu.Emacs", "CFBundleName"="Emacs", "CFBundlePackageType"="APPL", "CFBundleSignature"="EMAx", "LSASN"=ASN:0x0-0x4c24c2:, "LSBundlePath"="/Applications/Emacs.app", "LSBundlePathDeviceID"=16777220, "LSBundlePathINode"=39467589, "LSDisplayName"="Emacs", "LSExecutableFormat"="LSExecutable#!Format", "LSLaunchDLabel"="org.gnu.Emacs.6084", "LSLaunchedByLaunchServices"=true, "LSLaunchedWithLaunchD"=true, "LSLaunchEventRecordTime"=354943849105239, "LSLaunchTime"=now-ish 2019/10/21 14:33:40, "LSParentASN"=ASN:0x0-0x25025:, "LSWantsToComeForwardAtRegistrationTimeKey"=true, "pid"=47579 }