My dad has a green card and will always come every 5 to 6 months never crosses that limit but for the last few times immigration officials will always quiz him about his job out of the US and why he hasn't immigrated as yet.(He's only had his card for almost 5 years) This time he's been out for 4.5months and the guy insisted that he needs to apply for a white passport or something like a reentry for his next trip otherwise they will revoke his green card. Can they do that although he comes every 5-6months?

The minimum is every 6 months, but if that is his pattern, the CBP officer has every right to inquire as to his intention to be or remain an LPR. He was given good advice, in that if he is out of the US for such long periods (over 3 months) and is in the US for a short period, he should file for a re-entry permit (I-131). It looks like a US passport, but is white. It is valid for 2 years and generally can be extended once.

Your father should maintain ties to the US: house, filing income taxes, bank accounts, drivers license, insurance, family members, employment, etc.

Without the exact timeline of physical presence, it sounds like he is not qualified to file for naturalization (citizenship). He must be a LPR for 4 years 9 months, but also, he must be physically present in the US for 30 of 60 months preceding the filing of the N-400. It sounds like he's not in the US much, so he will need to stay in the US for about 2 1/2 years before being eligible.

Also remember the 90 day jurisdictional requirement for the N-400 filing. Consult with an immigration attorney, not a difficult issue. Good luck.