Again, Nadine, spank him a little. Tell them that the offer you made on their place drops by X amount per day. I think 1,000 is a nice round number, for Y amount of days. You probably won't get the property, but if you do, you will get it at a sweet discount. And either way, win it or lose it, you will feel great about yourself psychologically.

Go get 'em.

Hi Nadine, the reason you have a Realtor is so YOU don't have to worry. Listen to your agent and in a few days if you don't get any answers recind your back up offer and move on. Three weeks with no progress in todays market can be a red flag. OR, make them perfectly aware that your offer is only good until a certain date and stick to it.

Three weeks seems like a long time for a cash offer to fly or fail. Usually there is a period of a week or so to verify that the funds are available. There are home inspections and negotiations regarding those inspections, as well as title work.
What is your agent telling you? Your agent should be talking with the listing agent to see when that agent thinks this deal will sink or swim.
Good luck. But don't stop looking...you may miss another dream home.