How many times can bonding be applied to the front teeth?

If the bonding has failed three times, it  might be time to transition to a veneer or crown.  This would be determined by the amount of tooth structure remaining.  Photos would help to give you a definitive answer .  

As long as your tooth has the structure to bond to, you can bond as many times as you like. Obviously the more times you bond to your tooth, the weaker your tooth may become. Eventually your tooth will need a crown after too many bonding episodes.