Sine fide amicitia diu manere non potest.

Because sine is a preposition that takes the ablative in Latin. So:

• sine = without
• fide = ablative singular of fides, fidei = faith, trust, loyalty

Together, sine fide means without faith/trust.

Amicitia is nominative singular, because it is the subject of the sentence.

The sentence is saying that friendship cannot remain for a long time without trust. So amicitia is the thing doing the action of manere (to remain).

Because its subject, amicitia, is singular.

• amicitia = friendship (singular)
• potest = is able / can, 3rd person singular

So potest agrees with amicitia.

Manere is a present active infinitive, meaning to remain or to last.

It goes with potest:

• potest manere = can remain

This is very common in Latin: a finite verb like potest is followed by an infinitive.

Because non normally negates the finite verb. Here the finite verb is potest, so:

• non potest = cannot

Latin word order is flexible, but non potest is the most straightforward way to say is not able / cannot.

Diu is an adverb, meaning for a long time or long.

It modifies manere:

• diu manere = to remain for a long time

So it tells us how long the friendship can remain.

Latin often leaves the subject unstated only when the verb ending already makes it clear. But here the subject is actually stated: amicitia.

English might say friendship cannot remain... or it cannot remain... depending on context. Latin simply uses the noun amicitia as the subject and does not need an extra pronoun.

All three are possible depending on context, because fides has a broad meaning in Latin. In a sentence about friendship, trust or loyalty is often the most natural sense.

So sine fide amicitia is best understood as something like:

• without trust, friendship...
• or without loyalty, friendship...

Latin word order is much more flexible than English word order because the endings show the grammatical relationships.

A very literal rearrangement into a more English-like order might be:

• Amicitia non potest diu manere sine fide.

That would mean the same thing.

The original order puts sine fide first, which gives it emphasis: Without trust, friendship cannot last.

They are:

• sine = without
• fides, fidei (f.) = faith, trust, loyalty
• amicitia, amicitiae (f.) = friendship
• diu = for a long time
• maneo, manere, mansi, mansum = remain, stay
• possum, posse, potui = be able, can
• non = not

Knowing the dictionary form helps you recognize why the sentence uses the forms fide, amicitia, manere, and potest.

Yes. In Latin, as in English, a singular noun can express a general idea.

So amicitia here does not have to mean one particular friendship. It can mean friendship as a whole or the state of friendship.

That is why the sentence sounds like a general truth: Without trust, friendship cannot last long.