Question: - How many times can I lift and replace the ball when on the Putting Green?
Answer: - No limit.
Rule 6-1b "A ball on the putting green may be lifted and, if desired, cleaned. The position of the ball must be marked before it is lifted and the ball must be replaced."
The rule does not state how many times the ball can be lifted. For this information we must see "Decisions on the Rules of Golf"
Decision on the Rules of Golf 16-1b/1
"Q. A player lifted his ball on the putting green under Rule 6-1b, cleaned it and replaced it. As the player approached the ball to play his next stroke, he feared that the ball might move. So he lifted the ball again, replaced it and played. What is the ruling?
A. There is no penalty providing the player marked the position of the ball both times. Rule 6-1b permits the lifting of a ball on the putting green for any reason."
This means you can lift the ball, for any reason, as many times as you feel necessary (providing that it does not unduly delay play).