ELSS - can we continue to hold beyond 3 years and gain tax benefits?

I have an ELSS tax saving MF) invested in 2016. It will qualify for completion of the necessary 3-year tax period this year (2019).
My question is - if instead of enashing the MF units, I continue to hold on to it for another 3 years, can I claim tax benefit again for the year 2019? In that case what will be the investment value to consider as MF value keeps changing each day?

OR am I mandatorily needed to encash the existing MF units, and then re-purchase it again to claim tax benefit?

Yes, you need to encash and buy again. Because encashing is at your discretion meagre keeping invested doesn’t count as 80c investment.
For tax purpose, only investment done or transaction done will be considered.

You can claim tax benefit only in the year you invested.