Ally requests after battle

Do you already have 50 allies? That box stops showing up once you reach the cap of 50.

Nope. 27/50

If you can find out their ally code, you can go to allies and search for their profile with that.

So there is no way to get that ally Invitation screen back up?

Is your ally list full? If so, remove a couple of less active / lower level allies.

That's not the reason, unfortunately. I have 27 allies currently.
Is it because I previously hit "NO" couple of times for that same ally ans now the system falsely tries to not bother me anymore?

It might also be, that the guy you want to add has a fully ally list.

Yes, thanks. I have not thought about that. Obvious.
Bad news though cause now I have to find another way to contact him.
I wished the chat system would allow to directly message him.

If he is top 50 can you find him in the "ranks" screen and message him from his profile there?

Yes he is top 50 but those buttons are inactive (can not click them).
So I had thought I add him to allies and invite him to a channel.

Edit: I do have a feeling that there is a reason that getting in touch with shard mates in-game is so difficult...