Correct. He that exercises a saving faith possesses the irreversible gift of God, and cannot lose his salvation.
If one has to do something more to keep the gift than just to gratefully accept it, that would necessarily be a works-based "salvation" which would be no salvation at all. And it would be another gospel about another christ.
Read the Book. 2 Cor. 11:3-4
So...
bottom line:
Are we saved by faith; and kept by it?
or are we...
Saved by Faith; Kept by Works?
Before someone says Undistributed Middle; I’ll lay out the other two possibilities (that NO one seems to claim):
Are we saved by Works; and kept by them?
or are we...
Saved by Works; Kept by Faith?