Quamvis periculum maneat, mater dicit spem servandam esse.

Because quamvis here means although / even though, and in Classical Latin it is very commonly followed by the subjunctive.

So:

• quamvis = although
• maneat = may remain / remains in a concessive clause

This is called a concessive clause: the speaker admits one fact, but then goes on to say something else anyway.

So Quamvis periculum maneat means something like:

• Although danger remains
• Even though the danger is still there

The subjunctive is required by the conjunction, not because the action is unreal.

Here quamvis means although or even though.

A learner may know quamvis in other contexts as as much as you like or however much, but in sentences like this it functions as a conjunction introducing a concessive clause.

So in this sentence:

• Quamvis periculum maneat = Although danger remains

That is probably the most natural way to understand it.

Periculum is nominative singular neuter, because it is the subject of maneat.

Breakdown:

• periculum = danger
• maneat = remains / may remain

So literally:

• danger remains

That is why the nominative is used.

Because spem is accusative singular, and it is the subject of the infinitive phrase servandam esse in indirect statement.

After verbs like dicit (says), Latin often uses:

• accusative + infinitive

So instead of saying:

• mater dicit quod spes servanda est
  Latin more classically says:
• mater dicit spem servandam esse

In that construction:

• spem = the thing being spoken about, in the accusative
• servandam esse = to have to be preserved / that it must be preserved

So spem is accusative because it is the subject of the infinitive inside indirect statement.

Yes. This is a standard accusative-and-infinitive construction.

Main clause:

• mater dicit = the mother says

What she says:

• spem servandam esse

That whole phrase is the content of her statement.

So Latin uses:

• spem = accusative subject
• esse = infinitive
• servandam = gerundive agreeing with spem

This is one of the most important Latin patterns after verbs of saying, thinking, knowing, hearing, and perceiving.

It is a passive periphrastic inside indirect statement.

More specifically:

• servandam is the gerundive of servare
• esse is the infinitive of sum

Together they express necessity or obligation:

• servanda est = must be preserved
• servandam esse = to have to be preserved / that it must be preserved

Because this is inside indirect statement, Latin uses the infinitive esse instead of the finite verb est.

Because it agrees with spem.

Spes, spei is a feminine noun. In this sentence, it appears as spem, which is:

• feminine
• singular
• accusative

The gerundive must match it, so we get:

• servandam

not:

• servandus
• servandum
• servanda

Agreement is the key point:

• spem servandam esse = that hope must be preserved

Because spem servare would mean something different.

• servare = to preserve
• spem servare = to preserve hope

That is just a plain infinitive phrase about the action itself.

But servandam esse adds the idea of necessity:

• spem servandam esse = that hope must be preserved
• that one ought to preserve hope

So the sentence is not merely reporting an action; it is reporting a judgment about what must be done.

The sentence does not state the agent explicitly.

In a passive periphrastic, the person who has the obligation can be expressed in the dative:

• nobis spes servanda est = we must preserve hope / hope must be preserved by us

But here no such dative appears. So the idea is more general:

• hope must be preserved
• one must preserve hope
• hope should be maintained

The responsible person is left unstated, and English often translates this with a general must or should.

Yes. Although it is formally passive, English often translates it more naturally with an active expression.

Possible translations include:

• that hope must be preserved
• that one must preserve hope
• that we must keep hope alive
• that hope should be maintained

All of these can represent the Latin well, depending on context.

• dicit is present tense: she says
• esse is a present infinitive

In indirect statement, the infinitive’s time is understood relative to the main verb. Here the sense is usually simultaneous with dicit:

• mater dicit spem servandam esse
  = the mother says that hope must be preserved

So the necessity is presented as current at the time she speaks.

Latin word order is much more flexible than English word order. The sentence is arranged for emphasis and style rather than strict positional rules.

Here the structure is:

• Quamvis periculum maneat = concessive clause first
• mater dicit = main statement
• spem servandam esse = indirect statement

Placing Quamvis periculum maneat first sets up the contrast:

• Although danger remains...

Then comes the main point:

• ...the mother says that hope must be preserved.

This is a very natural Latin arrangement.

Yes. The sentence has a clear concessive contrast:

• periculum maneat = danger still remains
• spem servandam esse = hope must still be preserved

So the idea is:

• even though there is still danger, that does not cancel the need for hope

Latin often uses quamvis clauses this way: to concede a difficulty and then assert the more important point.