I know it may seem random at times, but there is a
consistent logic running through the manga that explains why some nations live
on despite ceasing to exist politically. The reason that this causes a lot of
confusion among fans is because of how loosely the word nation is defined in
Hetalia.

Nation doesn’t strictly mean an autonomous and politically
recognized sovereign state. Instead, personifications exist as representations
of a group of people and their culture, hence explaining their wide diversity
(e.g., kingdoms, religious orders, micronations, city-states, provinces, etc.)
Remember that the modern nation-state is a recent phenomenon. Humans organized
themselves far differently in the past. Larger post on that here [x].

In “It’s a Treasure Box of Countries”, it’s confirmed that
the nations are cultural and citizen-oriented personifications. Two things can
happen when a nation dies.

1)  They gradually fade when their people’s culture
or identity (personality) disappears.

“Usually, when the culture of the country’s personality
dies/ disappears, the country would gradually disappear or entrust him/herself
to the country that takes over him/ her.

2)  The ex-nation becomes a state representative.

“Regardless if their people’s culture and
personality disappears, the personification can still live on as a state
representative.”

There are two points to take away from this. One, the
nations don’t cease to exist because of political recognition. First and
foremost, they exist for their people and their culture. Two, nations don’t
necessarily die right away, or at all if they decide not to.

Ex: In World Stars, France reaffirms again that the nations exist because of their people.

That said, let’s go through some examples.

Poland and  Lithuania: 

After the third partition of their empire, it wasn’t just
Poland that ceased to exist on the political map.
Lithuania did as well. Nonetheless, as Lithuanians and Poles were absorbed by
Russia, Prussia, and Austria, thus ending their political identity, their
cultural identities remained in tact. Lithuanians and Poles didn’t disappear; their states did.

It’s for this reason on top of the fact that nations gradually
disappear that Poland and Lithuania are revealed to have lived during this era.
Poland made friends with Italy and bonded over their desire for independence.
Meanwhile, Lithuania became a servant to Russia.

Holy Rome:

Holy Rome didn’t die right away despite being dissolved,
once more demonstrating the gradual pace of how and when a nation fades.

Prussia:

Larger post covering him here [x].

Whether he’s East Germany or not, it’s clear that Prussia is
losing his immortality.

Ex: When Germany’s dog bites him, Prussia takes longer to
heal from a wound.

When asked on whether Prussia will disappear, Himaruya doesn’t rule this out as a
possibility [x].

In sum, it’s important to note that the nations don’t exist
for political reasons. If they die, it’s because their people no longer
identify under a common identity, or their culture disappears. This death doesn’t
occur immediately and is a gradual process. On the other hand, personifications
can still choose to exist even without a group of people and culture to
represent.