You can get a report of how many API calls Rocketship is making to your Autotask via the API Activity by Hour feature in Autotask:

  1. Log into Autotask as an Admin
  2. Click on Admin->Extensions & Integrations
  3. Click on Other Extensions & Tools->API Activity by Hour
  4. Choose the target Date in the Date field
  5. Click Search

You can download the results as a CSV via the Export icon.