Can Old-Timers die?

I have A 19 year old Ojitchi.

Will there be a point in where it dies?

It can die. I remember I had an old-timer

and it died.

As far as I know old-timers can die. I'm not sure at what age exactly, though.

It will die if you leave it alone for a few days. Old-Timers like Ojitchi, Oyajitchi and Otokitchi die at a certain point, but it's either you didn't care for it correctly, or it's time for it to die. Usually, if you take care of an oldie Tamagotchi, it might be able to live for a few short years. On a V4, for example, if your Tamagotchi isn't married, "it will grow old until it passes away". Scientifically speaking about your Tamagotchi, your Tamagotchi has morphed into an oldie, and it will die in a few short days.

Short? SHORT? I have had my Tama for WEEKS now! >.<

It doesn't have to be a short time - I've had an old timer live to be in his 30s. It just depends on how you take care of them, as with all tamas. If you neglect an old timer for too long, it will die just like any other tamagotchi.

Characters on modern Tamagotchis (such as those in the Connection-series, or MusicStar, or Tama-Go) won't die of "old age". It's possible to keep them alive for months and months. However, they can die if neglected.

So I have to neglect my Old-Timer if I want to get a new one?

Which model Tamagotchi is your Ojitchi on? Depending on which model you have, you may be able to mate him, and move on to the next generation. On the earlier Connection versions, it's necessary for old timers to mate by connection (the matchmaker won't visit him / he can't visit the matchmaker.) On the more recent models, old timers can visit the matchmaker (or the matchmaker can visit him).

I think my oldest old-timer was 36 when he died, and that was on my V3.

is the death screen the same if you neglect your tamagotchi and if it just dies of old age but is well taken care of? because lets say you take really good care of your music star, it doesn't really make sense if it gets angry and packs its stuff and leaves (the supposed death screen) if you're taking really good care of it right?