Serva respondet se pulvere et luto iam fessam esse, sed ad verrendum paratam manere.

Because this is an indirect statement after respondet.

In Latin, when the subject of the reported statement is the same as the subject of the main verb, Latin normally uses the reflexive pronoun se:

• Serva respondet = the slave-girl answers
• se ... esse = that she ... is

So se refers back to serva.

If Latin used eam, that would usually mean her in a non-reflexive sense, referring to some other female, not back to the speaker/subject.

It is the accusative-and-infinitive construction, the normal Latin way to express an indirect statement after verbs like:

• dicit = says
• putat = thinks
• audit = hears
• respondet = answers

So:

• se = the subject of the reported statement, put in the accusative
• esse = the infinitive to be
• fessam = predicate adjective agreeing with se

Literally, Latin says something like:

• The slave-girl answers herself to be tired

but in natural English:

• The slave-girl answers that she is tired

Because it agrees with se, which refers to serva.

In an accusative-and-infinitive construction, the subject of the infinitive is in the accusative, so any adjective describing that subject must also be in the accusative.

Here:

• serva is feminine singular
• se refers to that same person, so it is understood as feminine singular
• therefore fessam must be feminine accusative singular

So the agreement is:

• se ... fessam
• se ... paratam

Both adjectives describe the slave-girl.

Because there are really two reported ideas after respondet:

1. se ... fessam esse
   = that she is tired

2. (se) ... paratam manere
   = but that she remains ready

So both infinitives depend on respondet.

Latin often does this when one verb of saying introduces more than one part of a statement.

Also, manere is not just a substitute for esse. It adds the idea of continuing or remaining:

• paratam esse = to be ready
• paratam manere = to remain ready / stay ready

Because Latin often leaves it understood when the subject stays the same.

The full idea is:

• Serva respondet se ... fessam esse, sed se ad verrendum paratam manere.

But once se has already been given, Latin can omit it in the second half because it is obvious that the same person is still meant.

So the sentence is more compact, but the sense is still:

• that she is tired, but remains ready

It is in the ablative case, and it explains what she is tired from or because of:

• pulvere = by/from dust
• luto = by/from mud

With words like fessus, Latin often uses the ablative without a preposition to express the cause or source of weariness.

So pulvere et luto fessam means something like:

• tired from dust and mud
• wearied by dust and mud

A native English speaker often expects a preposition like from, but Latin does not need one here.

Iam means already or by now.

It modifies the idea of fessam esse:

• iam fessam esse = to be already tired

So the sense is that the tiredness has already set in at this point.

It does not naturally go with paratam manere here; it belongs with the first idea.

Because Latin often expresses purpose after paratus with ad + accusative, and one common way to do that is ad + gerund.

So:

• ad verrendum = for sweeping, or more naturally to sweep

This is a very normal Latin pattern:

• paratus ad pugnam = ready for battle
• paratus ad laborandum = ready for working
• parata ad verrendum = ready for sweeping

English usually prefers an infinitive here, but Latin often prefers ad + gerund/gerundive.

Here it is a gerund.

Why? Because it stands by itself after ad and does not modify a noun.

• ad verrendum = for sweeping

A gerundive would be an adjective agreeing with a noun, for example:

• ad pavimentum verrendum = for sweeping the floor

There verrendum would agree with pavimentum and would be gerundive.

So in your sentence, since there is no noun for verrendum to modify, it is best understood as a gerund.

It adds the idea of continuing in a state.

So:

• paratam esse = to be ready
• paratam manere = to remain ready / stay ready

That is an important nuance here. The sentence contrasts two things:

• she is already tired
• but she still remains ready to sweep

So manere helps make the contrast stronger.

A useful way to divide it is:

• Serva respondet
• se pulvere et luto iam fessam esse
• sed ad verrendum paratam manere

So the skeleton is:

• The slave-girl answers
  • that she is already tired from dust and mud,
  • but remains ready to sweep.

Grammatically:

• Serva = subject
• respondet = main verb
• se ... fessam esse = first indirect statement
• sed ... paratam manere = second coordinated indirect statement

Seeing that structure makes the sentence much easier to read.

It may feel unusual from an English point of view, but it is very normal for Latin.

Latin word order is much more flexible because the endings show the grammar. So Latin can place words for emphasis or rhythm instead of following a fixed English-style order.

For example:

• se pulvere et luto iam fessam esse
  puts the ablatives pulvere et luto before fessam, grouping the cause near the adjective.

• sed ad verrendum paratam manere
  places the purpose phrase ad verrendum before paratam, which is also natural Latin ordering.

A learner often wants to rearrange everything into English order immediately, but it is better to notice the endings first and then build the sense from them.