If it is an REO, it can take time for the bank. The bank typically needs approval from investors or a board to move forward, plus you have a listing agent involved which actually makes 3 parties instead of two.
When making an offer, you should be making an offer that is realistic based on what you want to pay and the homes value. If you low-balled it, they may simply ignore it and wait for other offers or are already evaluating all offers. Worse, is that even if you do go back with a higher offer, they may accept a lower offer for various reasons such a no contingencies, cash, fast closing, etc. If you find a desirous home, you should be working with your agent to determine a reasonable offer based on repairs, condition, etc. You should be fairly close to the banks valuation (BPO) and you should place your offer accordingly based on what you are willing to pay unless there are unusual circumstances and you think you can justify offering far less than what the bank wants. Most banks are no longer giving away properties and have a fairly good idea of the local market. Your agent should be able to call the listing agent and get an update. If they haven't, ask them to call and get you one.