You'd eventually end up stuck is the problem.
Assuming we are going with the "you can't die no matter what" kind of immortality, loved ones dying is the least of your problems.
You'll end up floating in space or stuck in a black hole. Or possibly way before that, buried under tons of earthquake rubble, or whatever. Being trapped for eternity would be your fate.
So no thanks to immortality where you cannot die no matter what.