You may be able to make contributions to your HSA for 2016 until April 18, 2017. If you fail to be an eligible individual during 2016, you can still make contributions, up until April 18, 2017, for the months you were an eligible individual. See 2016 Publication 969 - IRS.gov
Last-month rule. Under the last-month rule, if you are an eligible individual on the first day of the last month of your tax year (December 1 for most taxpayers), you are considered an eligible individual for the entire year. You are treated as having the same HDHP coverage for the entire year as you had on the first day of the last month.
Testing period. If contributions were made to your HSA based on you being an eligible individual for the entire year under the last-month rule, you must remain an eligible individual during the testing period. For the last-month rule, the testing period begins with the last month of your tax year and ends on the last day of the 12th month following that month (for example, December 1, 2016, through December 31, 2017).
If you fail to remain an eligible individual during the testing period, for reasons other than death or becoming disabled, you will have to include in income the total contributions made to your HSA that wouldn’t have been made except for the last-month rule. You include this amount in your income in the year in which you fail to be an eligible individual. This amount is also subject to a 10% additional tax. The income and additional tax are calculated on Form 8889, Part III.
