For some meds, you need to be monitored for potential side effects and/or for resetting of the dosage. Medical conditions might also require monitoring and you need to consider a medical exam to check for other conditions or complications. Review your travel plans with your doctor and reach an agreement for future care.
If you are a full timer on the road for years, you will need to periodically find new providers. You also need to carry documentation of previous visits and labs.
If you need a prescription renewed, that can be pretty easy especially if you use a chain pharmacy. You doctor can call in a prescription for most meds almost anywhere in the country.