Attunement required once for all non-automatic abilities (constant or environmentally triggered).
Depending on success, one or more abilities are accessible.
Once an ability can be used, it can be used, period.
Exception is if the ability is controlled by the item, or by an entity bound into the item. In this case, attunement only allows to communicate with the ability controller. Negotiation is required afterwards.
If an ability is not discovered, new attunement rolls are only possible if circumstances change, either for the character or for the item (new knowledge, new magical environment...).