What was the contingency you missed?
Where is the property?
Have they already rented it?
Let me know, depending on your answers you may still have a chance!

Did they rent it out or did they just decide to put it out for rent? If the latter is true, just go back to your agent and ask them to resubmit your bid without the contingency. If not, find yourself another place. The one thing you don't want to do is become obsessed with a given property or you will pay a lot more than what you could get it for.

I would have your buyers agent stay in touch with the other agent. The real question is why in todays market would they take the house off the market if they had contract. I would recommend to keep looking for another home.

Sellers are the only people who could answer this question. You need to find a way to ask the seller -- perhaps use the same method you used to submit your offer. It is unlikely that there was a cause and effect relationship here. Seller probably had a time window within which to sell or else rent it out and that seems to have happened here.

If they have entered into a lease agreement they are required to honor said lease agreement unless they buy out the tenants lease prior to lease expiration. What do you think about offering more to the seller in hopes of chaging sellers mind to sell with a appraisal contingency attached.

Have an agent call the owner to see if they would consider selling the home.