How many times we can pillage or battle each region without using the Tyr's Challenge card ("As your action, you may pay 2 rage to repillage an already pillage")? Is there a limitation?
The rules for Blood Rage describe the phases of play, in particular with page 17:
To Pillage, choose a province that has at least one of your figures in it (or in a supporting fjord) and has not yet been successfully pillaged this phase (its Pillage token is showing the reward side up).
Ipso facto, each province may be pillaged repeatedly until a pillage is successful, and then it cannot be pillaged again.