Learn Farsi: شش ماه است که او وفاداری خود را نشان می‌دهد. - He has been showing his loyalty for six months.

This is the standard way to express an action that started in the past and is still happening. Instead of a complex perfect continuous tense like in English, Farsi uses the literal structure 'It is [time] that [present tense]'. So, it literally translates to 'It is six months that he shows his own loyalty.'

Why is the word خود used here instead of a possessive ending like اش?

خود means 'self' and acts as a reflexive pronoun. Whenever the possessor is the same as the subject of the sentence (he is showing his own loyalty), using خود is very common and natural, though saying وفاداری‌اش would also be grammatically correct.

Why does the direct object marker را come after خود instead of right after وفاداری?

The marker را must always come at the very end of the complete noun phrase that makes up the direct object. Here, the entire direct object is وفاداری خود (his own loyalty), so را attaches to the end of that whole phrase.

Can I leave out است که and just say 'for six months' using a preposition?

Yes! Another very common way to say this is by using از (from/since) along with پیش (ago). You could drop است که and say او از شش ماه پیش وفاداری خود را نشان می‌دهد which literally means 'From six months ago, he is showing his loyalty.'