But you haven't.

In your example, you are:

2015: Gold - > Platinum [based on 2015's flights/segments]
2016: Platinum [based again on 2015's flights/segments]
2017: Gold -> Platinum [based on 2017's flights/segments]
2018: Platinum [based again on 2017's flights/segments]


In your example, you only achieved the criteria for Platinum twice - during 2015 and again during 2017. That means that you would start 2017 as a Gold [even if you managed to qualify for Platinum again in the first 3 months of 2017, before your "old" status expires].

You must have ten consecutive years of earning Platinum within each calendar year, January-December. Earning platinum in the first 3 months of every other year will NEVER give you platinum for life (even if, as you say, you technically are platinum the entire time - given that the status of your card "lags" the calendar year by 3 months). You must put together ten consecutive years of reaching platinum in each calendar year. If you let any calendar year go by in which you don't earn platinum - and this is the case for you in 2016 in your example - then you break the chain, and your "lifetime years" clock reverts back to zero.