Having to constantly find new hiding places for the blood chalice, and keeping up with all the latest scanning methods so you can develop countermeasures. Your secret is never truly safe.

You know how the curse of pet ownership is that you will almost certainly outlive them?

That, but with everyone you love

All the people trying to dissect you for science.

Without getting into the heat death of the universe and all that, I can think of something that happens much, much sooner. I'm only middle aged and I already don't like where the world is going. Can you imagine being centuries, or eons past the era you identified with? Can you imagine how insufferable young people and old people alike would seem when you have centuries worth of life experience and wisdom? Can you imagine a horde of little edge lords on the internet confidently yet incorrectly telling you about the signing of the Declaration of Independence, when you were there when it was signed?

Loneliness. I think being immortal would show someone what true Loneliness is

The Sun will eventually fry all life on Earth and boil off the water & atmosphere. Eventually the Sun will die out completely, leaving you on a cold, dark rock.

Having to keep track of that evil snail.

https://www.reddit.com/r/AskReddit/comments/5ipinn/you_and_a_super_intelligent_snail_both_get_1/

The eventual heat death of the universe would be painful

Boredom after some period of time, you will have some everything there is to do.

On one hand, you have eternity to come to grips with everything you've done. On the other hand, it might take eternity to come to grips with everything you've done.

Seeing all of your friends and family die, knowing you'll never stop missing them.

Having the perspective of centuries. Seeing society make the same mistakes over and over again because they forget, but you never do. It would drive me mad. Already does, considering I have the ability to, and have, read history. I just imagine living it over and over to be tedious.

I don’t think you’d remember a break up from hundreds of years ago, let alone be upset about it.

I wonder if it might engender an advanced sort of solipsism and callousness towards other people. After thousands of years of the world coming and going around you while you remain, would you even recognize other people as real or meaningful?

Government Bureaucracy.

Renewing a driver's licence or passport. The individual looking at your application will see the date of birth and raise a red flag.

If other people are also immortal, the awkwardness of all of them eventually becoming your exes

Just depression in general. I don't want to live one lifetime, let alone never being able to die.

If you're immortal in a body that isn't broken then that might be a different story, but you'd still grow to love people only to have to lose them and go through that pain over and over.

As we get older, our perception of time speeds up. An immortal would easily lose track of time after just two human lifetimes, causing an immortal to suffer from dementia-like symptoms where they expect one date but find themselves habitually late. And since time doesn't mean the same thing as us to an immortal, they would eventually become disconnected from the world around them and be unable to reintegrate. They wouldn't be able to maintain friendships, relationships, mortgages, payments, etc. They would be surrounded by people but forever alone.

Not being able to kill yourself.

Being eaten by sea anemones, tuna, sharks, swordfish, sea turtles, penguins, and other jellyfish.

https://en.wikipedia.org/wiki/Turritopsis_dohrnii#Predation

The amount of shitting and wiping I d imagine you’d have to do, hemorrhoids would likely be unbearable overtime

Getting imprisoned for thousands of years unable to get out.