They started off. In keeping his self made promise going fast and not stopping, the hare took off and ran at top speed until he came to a broad river.
- promise going fast and not stopping
=promise (which was) to go fast and not stop
=promise (which was) going fast and not stopping
=promise going fast and not stop
Or
- In keeping his self made promise as he went fast and not stopped, the hare took off.
= In keeping his self made promise going fast and not stopping, the hare took off.
The original text (which is the source of the problem of the exam - textbook) was
They started off. In keeping his self made promise to go fast and not stop, the hare took off and ran at top speed until he came to a broad river.
But if analyzing this part in these two ways (above), I think 'going fast and not stop' is also correct. Is 'promise going fast and not stopping' gramatically incorrect?