Can a person that has once applied for a k-1 visa, and been approved, and then the lady from the Philippines goes back home apply again?

I assume that by the word "person", you are speaking of the petitioner, and asking whether he can apply for another person under the K-1 fiancée visa when the fiancée has gone back home. Depending upon your particular circumstances, this is a situation in which U.S.C.I.S. may request a waiver as its memorandum on the subject states that if a petitioner previously had a K-1 visa petition approved within two years prior to the filing a new petition, the petitioner must request a waiver. Thus, if your previous petition was approved within two years of filing a new K-1 petition, a waiver would likely be requested. There is some question concerning the legality of U.S.C.I.S.'s interpretation, but the prudent course would appear to be waiting two years after the K-1 approval before filing another. Please note that a waiver is always required if the petitioner has filed two or more K-1 petitions at any time in the past, regardless of the result.