At 5th level, an inquisitor can imbue one of her weapons with the bane weapon special ability as a swift action. She must select one creature type when she uses this ability (and a subtype if the creature type selected is humanoid or outsider). Once selected, the type can be changed as a swift action. This ability only functions while the inquisitor wields the weapon. If dropped or taken, the weapon resumes granting this ability if it is returned to the inquisitor before the duration expires. This ability lasts for a number of rounds per day equal to the inquisitor’s level. These rounds do not need to be consecutive.
So the way I feel it was meant to work is that the ability is limited to rounds per day based on inquisitor level which is how the linked answer also took it. But the way it reads to me is that you can use a swift action to activate Bane and it lasts for inquisitor levels, but doesnt have a usage amount. The ability has a stated starting action, changing action, and duration (which is important and different from how other classes are worded). It does not mention stopping the action (likely free, but this is countered by the ability remaining in effect when not in possession) or that the number of times you can use the ability is limited.
Similar class abilities are the barbarians rage, but it draws from a rage point pool, and you cant rage with an empty pool. A bard has their performance, but its also built around a point pool. A magus arcane pool is the closest Ive found, as it has a stated activation and duration, but also draws from a pool.
There are other class abilities that are number of times per day per class level but none of them occur to me at the moment for comparison.
So RAW, does the inquisitor have a limit on the number of times per day they can activate Bane?