Good question, not a easy answer. I camp 14 to 21 days unsupported and can Give you a cold drink on the last day, I can put ice in your cocktail for 14 day easy.
First use a chest just for drinks, prechill you drinks, I camp and surf in Baja, I put the drinks going into the chest in sea water to drop the temps. (80 air temp, ocean water 70, ice chest 34. dropping the 10 degrees helps save ice.) By using the chest for drinks you are not putting warm air into the food chest. this chest is used the most and opening it up is melting the ice. If you are NOT driving put as much melt water in the drink chest as possible, water warms slower than air. The 40 degree water will stay at 40 or so. When you open the chest the ambient air will replace the cold air and it will be rechilled when you close the lid. The less the air, the less that has to be rechilled. I will empty the food water into the drink chest when I change out the ice.
Second, use a box inside the chest to keep your ice in. I will start out with frozen h2o bottles in the bottom of the chest and block in the box. I try to keep the food dry. I'll also pre freeze H2O bottles put them with a food also. It's a pain the keep the food from getting waterlogged. I use the frozen H2O bottles for other fresh water uses. It helps to keep a ensolite foam top so add to the insolation.
Third, Ice chest with BLOCK ice and Dry ice. For 14 days I get 40# and fill the chest with blocks, whatever space I have in the chest is filled with proteins (Meats) and frozen H2) bottles. This chest is only open once a day. You pull the next days proteins and ice. keep this closed as much as you can. This chest too gets a ensolite foam pad.
Stuff: Keeping chest in the shade makes a difference! Keeping wet towels over the chest makes a big difference! When the first H2O bottles thaw swap the out for the ones in the dry ice. DO NOT PUT DRY ICE IN YOU FOOD CHEST!!! DRY ICE IS SUPER COOL AND WILL "F" UP ALL YOU VEGIES, AND BLOW UP ANY DRINKS. don't ask how I know this. You will need a icepick. The super chest add about 3 to 4 days, I love Maluna chest they sell direct on line. I get a extra day from their chest.
My guess is you are storing you drinks with you food, you will kill your ice in a hurry that way.
There are Ice houses that sell both blocks and dry ice. (look them up) The first time I saw a 100# block of ice and asked if we could just fill this up? it was pretty funny.