Appeal

This is quite odd. See if they acutally file their brief.
Ask you attorney

This is a question that really does need to be directed to your lawyer. There are many strategic reasons that what you are describing may be occuring. Your attorney should be able to answer all of your questions and help to come up with a strategy.

There are many reasons why this might occur. Some have nothing to do with strategy, i.e. the defendant may not be returning his lawyer's call), while others may involve an effort to gain an advantage in the litigation. You should contact your attorney to see if he or she can offer additional insight.

You should contact your attorney by telephone, and if he or she does not respond the same day, you should contact him or her via e mail or fax, or letter. You need to ask your lawyer whether or not the other attorney accepted the counter offer, and if so whether he accepted it in writing. If they did accept, then you should ask your attorney to have them tender the money AND dismiss their apeal. If they did accept the counter offer, then your attorney needs to send their lawyer a letter stating that payment and dismissal of the apeal is expected promptly. In Florida an appellant has 70 days from the date of the notice of appeal to file the initial brief. Often the appellant will ask for an extension of time to file. Tell your lawyer to advise the other side that he will not be disposed to agree to an extension (unless there has been a fould up with the clerk's office forwarding the record) of time if they do not get this resolved promptly.