The no response from server message happens during 1 of 3 things:
1. Dedicated server save file is large and the autosave takes more than a few seconds
2. Dedicated server is compressing the world file for sending to a new client (right as someone starts to connect)
3. Dedicated server has too many objects or entities to keep track of at once (think, loads of drills, grindwalls, 10+rocket launchers etc...)
If more than 1 of the 3 happen simultaneously, you'll get prolonged disconnects. The best suggestion is to limit the number of certain objects for your players. For example, limit the:
# of drills
# of turrets
# of grinders
# of refineries
# of pistons/rotors
Etc...
You also need to regularly run the maintenance script in the game panel making sure to take a backup of your world first.
Looking for a game server host known for brilliant 24/7 customer support and quality hardware?
Try a Pingperfect Space Engineers server today! https://pingperfect.com/gameservers/space-engineers-game-server-hosting-rental.php