I chose ‘если они не активны в течение…’ as ‘if inactive for...’ is just a part of the longer and the whole phrase: ‘Terminate old sessions if inactive for… 6 months’.

Or just 'если они не активны... 6 месяцев'

As long as we are dealing with "old sessions" in plural, we have to use "неактивны". And the phrase "в течение" is the best one to use before a period of time

There is no need in adding words like "в течение" ("during" ), "периода неактивности" ("inactive period") because they do not affect the meaning but complicate the phrase