Do you use FSRealistic ?
An user on the GSX creators server Discord reported a while ago that, when FSRealistic is loaded by the EXE.XML, the Couatl engine can't start automatically, even if it will work when started manually. Even if you don't have FSRealistic, another app might cause that.
That is, assuming you DO have the Couatl engine referenced in the EXE.XML. Its addition to the EXE.XML is done when installing GSX or when Relinking it. So, you might try Unlink/Relink in the FSDT Installer, so it will add again the EXE.XML lines, in case they have been lost for any reason.