If the ender dragon hits an End Gateway portal, it teleports out. Eventually a new ender dragon will spawn and the battle continues as if nothing happened, its health bar doesn't even go away. But if you teleport through the End Gateway, you will find the old ender dragon there.

I waited next to the gateway and got the dragon to fly through three or more times, and when I went through the gateway I saw three ender dragons nearby immediately make a beeline for the main island. I followed them in flight mode (even sprinting I was slightly slower than the dragons) and when we got back to the main island apparently one or more dragons despawned at some point but I was left with two ender dragons.

Steps to reproduce:
1.) make a platform immediately behind the gateway with respect to the main island
2.) sit on the platform in survival mode until the dragon begins to charge at the player
3.) position the gateway between you and the dragon
4.) dragon enters gateway
5.) enter gateway and observe duplicate dragon
optional: follow dragon back to main island