I do not have experience with Avalara or access to an Avalara account to confirm, but my guess would be that Avalara's Invoice functionality runs in a User Event script deployed to the Invoice record, and I'll guess your automation is a User Event on the Sales Order and/or Item Fulfillment. The two User Events will not chain as actions in User Event do not trigger subsequent User Events.
If that's all true, then whatever process you have which modifies the Invoice and needs to trigger Avalara cannot execute from a User Event. You'll have to move it to a different script type; the usual suspects are a Suitelet or Map/Reduce.