As far as I know a listing agent can not stipulate any issues. It is the seller that responds to the counter offer. I believe the seller can require that a buyer use a certain lender.
In California we have a 17 day contingency period to do all investigations on homes, get a loan approval, read disclosures, and home appraisal. Also, in our contracts is an interest rate clause that states if your interest rate increases above "x" you may be able to cancel the escrow.In terms of cancelling the transaction related to decline in home price this may become an issue with your appraisal. If the appraisal comes in low you can cancel the escrow also if the bank doesn't reduce the initial offer price to the present appraised value.Within the 17 days if an issue comes up with your physical inspection, HOA disclosures or seller's disclosures you may cancel the transaction as well. Just to clarify these are transactions based in California.
What you may want to do is renegotiate down to the appraised price. The bank realizes that you submitted an offer that won't appraise.