Learn Turkish: İtirafı gelmediği takdirde dava uzar. - If his confession does not come, the case drags on.

This structure uses the negative verb stem gelme-, adds the participle -dik, and then the 3rd person possessive -i, which softens the k to ğ to make gelmediği. Followed by takdirde (in the event of), it literally translates to 'in the event of its not coming.' This is a highly formal way to express a condition.

Is the -ı on itirafı the accusative case suffix because it is the object of the verb?

No, it is the 3rd person possessive suffix, making it 'his confession' (or her/its confession). In this sentence, itirafı is the subject of the action gelmek, not the object. It is 'his confession' that is not coming.

Could I just use the standard conditional gelmezse here instead?

Yes, itirafı gelmezse means the exact same thing and is much more common in daily conversation. The phrase gelmediği takdirde is formal, but it fits perfectly here because dava (lawsuit or court case) sets a legal, official context.

Why use the aorist tense uzar instead of the future tense uzayacak?