Banks seek 2 things in these transactions, best net price and ease/speed of transaction.

For the first issue (net sale price), make sure your offers are priced right through your agent and unless its absolutely necessary, cut down on the concessions you're asking for. Remember that the bank is losing money on the vast majority of these transactions so they want to give up as little as possible. The less you ask the bank to pay for, the less the bank loses and the stronger your offer is. Some of the smaller concessions like transfer taxes and home warranties may add up to $1k-$2k but it may also mean the difference between you getting the house of your choice and not getting it.

For the second issue (ease/speed of transaction), what type of financing do you have (Cash, Conventional, FHA, VA)? Banks prefer them in the order that I listed them so if you have an FHA offer sometimes you'll find yourself losing out to Conventional or Cash offers repeatedly. If you're an FHA and its at all possible, try asking your loan officer to qualify you for a Conventional loan. It will require a slightly higher down payment but it will greatly increase your chances of your offers being accepted.