This is a good question, and the answer can go a few different ways. First off, if things change with your financing to the point that you need to back out of the transaction, you are generally eligible to receive most or all of your good faith deposit money back if you cancel during the contingency period, which is customarily the first 17 days of the escrow. However, if your loan has not been fully approved by the time you need to remove your contingencies and you do so without the assurance that your lender can commit to closing the loan, then you could run into trouble. All of the terms of the buyer's rights as it relates to your good faith deposit should be spelled out in the first two pages of the Residential Purchase Agreement form (your offer).
Another option you can always consider if the requirements for your FHA loan change, is that you may still want to complete the transaction. It will depend on the specifics of your situation. Talk to your agent and mortgage professional about these issues, as they should be knowledgable about what your rights are as it relates to this. Good luck!