Cant leave planet Elaaden

T only works while in the Nomad.

You can also go up the ramp to the Tempest and press E when you see the prompt.

I had the same problem. I tried reloading old saves and switching my loadout to try to get the map to reload but no luck. Frustrated thinking I would have to load a really old save to get myself out of this bug I jumped into one of those craters that would cause my character to leave the mission area. Upon reload I was able to get access back to the Tempest. I hope that helps anyone else with this issue. 

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@Pilali wrote:

I jumped into one of those craters that would cause my character to leave the mission area. Upon reload I was able to get access back to the Tempest. I hope that helps anyone else with this issue. 

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Yup, that generally works if stuck "out of mission" in open world. Die in some fashion (jumping off a cliff is easiest) resets the map/variables and should bring things back to normal.

Same here...

In fact other thing that happened to me was a infinite loading situation inside a remnant chamber where you can find a remnant data core... going south from the western monolith.

In this situation I forcefully exited the game, entered again with the latest autosave and the game loaded inside the chamber, with the nomad within (weird).

I have all the savegames to provide if that helps with the troubleshooting.

For me dying didn't worked the classical way - being killed by enemy or jumping off from mountain/hill (jumping off especially since you are saved by hydraulic suspension in your gear that helps you survive high altitude jumps, and knowing that mountains aren't straight pillars, meaning that you wont fall the whole height of the mountain, you will land on a nearby side of the mountain since you have not enough distance from it to make that vital landing, so you will not die from a jump).

What worked for me was when I was in the sinkhole, I had this bug that loading autosave I got into sinkhole in order to get that mining drone in it because of developer lack of attention, so after I got out by teleporting to some forward station, I couldn't get back on Tempest no matter what, so I read here solutions and I tried all the ways I could die which didn't helped until I tried to reset myself by driving in a sinkhole again, which reset the bug because out of mission zone thing, so probably it can either be reseted by going in places that will throw you back on the map with the automatic reset from out of mission zone places.

I'm currently having this issue. I've completed every mission on Elaaden, but every time I try to get on my ship to leave I get stuck in a neverending loading screen. I've tried suicide, I've tried using Y while inside the vehicle to call my ship to me, I've tried walking right up to the ship, I've gone off and done other missions hoping the issue would resolve itself, I've restarted my Xbox, I've closed and reopened the game, and nothing has worked.