Please see this Turbo Tax FAQ on the transmission server error.
https://ttlc.intuit.com/community/bugs-and-error-messages/help/turbotax-online-error-your-transmission-did-not-go-through-due-to-a-server-problem/00/27609
Can you please let us know which state you are filing a tax return for so we can check into this further?
I'm also having this issue while trying to eFile federal and North Carolina tax documents.
For me the issue was the form being unavailable.
I found the answer in a different forum post:
After Googling around I found a page containing all of the forms' availability.
https://proconnect.intuit.com/proseries/forms-finder/
It would really be nice if the error message explained what the actual problem is, but TurboTax is becoming less user-friendly every year.