[susan53]

It's not just successful, but the whole word family - succeed and success too.

We didn't succeed in repairing the car.
I didn't have much success in persuading Jane to come with us.
He was successful in obtaining a conviction.

Here, the person is talking about specific actions, expressed through a gerund, and in is essential. You couldn't use at

But if you're talking about an activity in general, then at becomes more likely than in:

I was never very successful at making cakes.
He's successful at everything he does.
I never succeed at chess.


But more likely - not obligatory. There are lots of examples of in with general activities too :

He's never been successful at/in forming lasting relationships.
She is more likely to succeed at/in at/in scientific subjects than at/in the humanities.

One thing to keep in mind - just because in/at follow succeeed, success or successful, it doesn't necessarily mean the preposition is dependent on that word. For example , in :

He didn't have much success in Rome.
in Rome is just a preposition of place, telling you where he was at the time. That may seem obvious, but other expressions are more sneaky - eg He's very successful at interviews . Does it mean He's successful when he goes to interviews (preposition of place) or He's successful at being interviewed (preposition dependent on successful).