I first entered the US in July 2014 to activate my green card. I applied for a re-entry permit and I then left in September 2014. My re-entry permit was eventually granted and I picked it up at the London Consulate in about November 2014. Interestingly, the consular officer told me that I could stay out of the US with the re-entry permit for two years from the date of its issuance (which was about two months after I had actually left the US). The implication was that, if I'd wanted to, I could have stayed out of the country for about 2 years and 2 months with that re-entry permit.
I returned to the US in June 2016. I stayed only for two weeks before leaving again and finally returning to live here permanently in July 2016. During both of those entries into the US (June and July), I showed my re-entry permit. Nothing was said, no questions were asked and I was simply stamped into the country. I have since left the US a further three times for work and holidays and have not carried the re-entry permit with me (which has now expired anyway). No one's ever asked me anything about my residence in the US, or my intentions, even when travelling with my partner, who has an H1-B visa.
For more visit this link.