If your current agent wants to give up on you and your search, that is his or her business decision, it does not have to be your decision. If you start looking with a new agent, be sure to identify to the new agent all properties that you saw with the first agent, to avoid a procuring cause (who earned the commssion?)
problem, should you decide you want to offer on a property that you saw with the first agent. Ask both agents in advance of such a situation how they expect you (and them to handle that situation) Be sure to get every one on the same page about that very important issue.
- Maybe you don't need to go every weekend, but it makes sense for you to see the new listings that are coming on and to be apprised of the market, in general.
If you received an offer on your own house and found the perfect replacement house the same week. That would be serendipitous. We need more serendipity in real estate these days.
First question; Is your house listed by a Realtor? If not, why not? (An excepted offer without first knowing if a professional lender has qualified the buyer does not sound like the work of a professional Realtor)
Second; Does your buyer agent have a firm understanding of what you want in your next home? If so, are they emailing you homes that come onto the market that meets your criteria? If not, why not?
Lastly; Hang in there! If your buyer agent knows you are serious about selling your home (and it sounds like you are) then they should help you at every turn. However, remember that your buyer agent has other clients and their needs have to be meet too. So do not expect your agent to show houses to you 4 times a week type of thing.