The Moon's orbit will decay to the point that solar eclipses are no longer possible in about 600 million years. The Sun will continue to rise and set following that point, in all likelihood.
This is however about the same time that the carbon-silicate cycle will have been disrupted to the point that C3 photosynthesis is no longer possible. Humans (or their descendant species) may not be observing either lunar or solar eclipses by that time, at least not from Earth.
And by 1.5--4.5 billion years from now, still within the main solar sequence, the Moon will have drifted far enough from the Earth that the Earth's axis is no longer stabilised by the Moon. By this point, even lunar eclipses might no longer be possible.
(The other factor is that the Moon drifts so far out that it orbits outside the Earth's umbra, such that total lunar eclipses no longer occur, though "blood moon" penumbral eclipses could still happen. I don't know what the timeline for this might be. But again, so long as the Earth itself rotates and isn't consumed by the Sun, sunsets will still occur.)
By 800 my to 1.6 by, solar luminosity will have increased to the point that life on Earth's surface is likely impossible.
Sidenote: Past events are designated using the abbreviations kya, mya, bya, etc., (thousand, million, billion years ago). I'm not aware of a standard abbreviation for time in the future, though it would seem kyf, myf, byf, etc., might be reasonably used for this. Or perhaps "kyp" or "kyn" (thousand years from present, thousand years from now).
