No, relations with the Philippines are not permanently harmed because Philippines President insulted Obama. He is still very new and getting used to being in power. He has been committing human rights violations and if they don't stop soon or something isn't done to rectify the situation, relations could potentially be permanently harmed.
Relations will normalize again. In fact, they should not have much effect on relations between the countries. The men need to get past their differences and do what is right for the respective countries. Name-calling has been around forever, and people need to get used to the concept of ugly politics already.
Many of the past US Presidents have not won the worlds' affection and have been verbally scorned. These are only words, the presidency changes and such verbal remarks are quickly forgotten. This would not be true if some physical action had replaced the verbal nature of expression and repercussions from that would be quick.
When the Philipene president steps down and a new president is elected he or she or they will begin the process of reparing relations between the US and the Philipenes. The regret of the current President goes a long way as well but he will need to truly apologize and stop saying terrible things.