あやうく忘れるところでしたって英語でなんて言うの？

I almost forgot is an expression to be used when you remembered something at the last minute but you almost did not remember it.
you could also say it almost slipped my mind, this has the same meaning.
 
It almost slipped my mind, thank you for giving me a reminder is a way to tell someone you almost forgot something and express your thanks.

To remind someone means to tell them something to make them remember it. So you would say 'Thanks for reminding me, i almost forgot!' this says thank you to the person as you would not have rememebered otherwise.
You can used the term 'Thanks for the reminder' or 'Thanks for reminding me' they mean the same thing

To slip one's mind means to forget something which you generally would remember.
Fo example, you may be answering question in a quiz and one of the questions is: 'When was the Battle of Hastings?'
In the UK it is a well-known historical fact that all schoolchildren generally know.
However, in the stress of the moment, you forget. The information has slipped your mind! And then you remember - it was 1066!

Thanks for reminding me, I'd forgotten.
I nearly forgot, thank you for reminding me.

These sentences are suitable in this situation.

The two sentences you see provided above are excellent ways to express thanks to someone for reminding you about something in particular. In the first sentence you will see the term slip one's mind. This term means to forget. This term is common in our everyday conversation and is appropriate for informal settings. It would make an awesome addition to your vocabulary!