I hate unanswered threads and also hate to respond to a thread that's 2 years old, but this continues to be an issue and I wasn't able to find any helpful hints or the proper solution.

Ran into this as I upgraded from 10.4.3 to 10.4.5.  No matter what I did, it still gave me the error. I ended up following this process:

1. Backup the following files and locations for both the DMZ and Forms Server:
   • DMZ Server
     • %programfiles%\Laserfiche\Laserfiche Forms\Forms\Web.config
     • %programfiles%\Laserfiche\Laserfiche Forms\Config\Web.config
   • Forms Server
     • %programfiles(x86)%\Laserfiche\Laserfiche Notification\Service\Laserfiche.PushNotificationService.Master.Host.exe.config
     • %programfiles%\Laserfiche\Laserfiche Forms\Forms\Bin\RoutingEngineServiceHost.exe.config
     • %programfiles%\Laserfiche\Laserfiche Forms\Forms\Web.config
     • %programfiles%\Laserfiche\Laserfiche Forms\Config\Web.config
2. Now uninstall Forms from both servers and delete those files (not the backed up ones, the ones in the %programfiles% area)
3. Set Forms back up, it should populate the default web config files and the other two service configuration files
4. At this point, both servers should be working and you should be able to access both the FormsConfig and Forms website - although /Forms will give you some error about not connected to database.
5. Now go to each FormsConfig and register Forms to the Forms Database. Please note, that there's also another issue where you have to register Forms to a temporary Forms Database, then re-register it to the correct database for it to work correctly. I did not run into this when performing a new install but did run into it once when I opted to perform a repair/stand-in-place upgrade.
6. After connecting Forms to the database, follow the whitepaper on setting up DMZ for Forms. Depending on your setup - you'd want to select the correct method to follow. Ref: https://support.laserfiche.com/resources/3481/hosting-laserfiche-forms-10-in-a-perimeter-network-dmz

The reason why you want to back up the old files above is in case you need to reference any of the Hostname settings or security settings that were set up.  There's something unique in the file that likely is changed every time forms is reconnected to the database and thus, breaking the connection.  I'd tried just reinstalling everything from scratch and just dropping the backed up files in their places - wouldn't work.

All-in-all, each time I upgrade or have to fix this - this was the only consistent process where I got it to work and the error to go away. It takes about 30 minutes for the entire process.