This is controlled by the settings of the style objects. There are a number of default styles in Author-it that have a None setting - List Continue, List Note, Wide Graphic, or you can create your own.
You should also check that the style has the appropriate outline level defined under the Style Definition tab. It is this outline level that determines the level of the list - lists at a lower level are reset by lists of a higher level.
For example, a list with the outline level 1, will reset the numbering of a list with the outline level 2, but a list at level 1 will not be reset by a list at level 2. A paragraph with no numbering or outline level will reset all lists.
Let's look at an example using the list styles:
List Number (uses outline level 1)