MSSQL - Running sum with reset after gap

This is a gaps and islands problem, and one approach uses the difference in row numbers method:

WITH cte AS (
    SELECT *, ROW_NUMBER() OVER (PARTITION BY PersonID
                                 ORDER BY Visit_date) rn1,
              ROW_NUMBER() OVER (PARTITION BY PersonId, Medication_intake
                                 ORDER BY Visit_date) rn2
    FROM yourTable
)

SELECT PersonID, Visit_date, Medication_intake, Previous_date, Date_diff,
       CASE WHEN Date_diff IS NOT NULL AND Medication_intake = 1
            THEN SUM(Date_diff) OVER (PARTITION BY PersonID, rn1 - rn2
                                      ORDER BY Visit_date) END AS Running_sum
FROM cte
ORDER BY PersonID, Visit_date;

Demo

The CASE expression in the outer query computes the rolling sum for date diff along islands of records having a medication intake value of 1. For other records, or for records where date diff be null, the value generated is simply null.