I have a business dispute with another person. We chose to arbitrate it before submitting our claim to local rabbi to be solved in beit din. However, arbitration already took four months and, in my opinion, leads nowhere. How long shall we arbitrate before submitting the claim to beit din?

Arbitration should not take longer than four months, unless the case is extremely complicated. Before submitting to Beit Din, ask the arbitrator if he is optimistic for a quick resolution. If he is , give it another 2 weeks.