Last time I sold my house (US, NC) we signed a listing agreement with our agent that basically said we were commiting to having her sell our house for x days and couldn't say pull out and get another agent until that time period was over.
Same thing happened to me. Long story short, the buyer is on the hook for the original agreed upon price. If the bank only agrees to loan price-x, and the buyer can't make up the difference, then their only option is to negotiate a lower price or drop out (and lose their due diligence deposit). If you really don't want to renegotiate/don't like the offer, then you should drop them, take the deposit, and get another buyer (which will have another bank, another appraisal, and might not be as low/buyer may be able to make up difference.)
How long did it take you to get the offer? What are you doing for your next place? Do you need the cash from the sale of the old place to close on the new place? Things to consider. You can always get another offer, just depends on your timeline how badly you want to hang on to the one you have.
If you do nothing, then they can't sell your house and you get to keep the deposit. Whether your agent is communicating or not. Just don't sign anything.