Vegetable gardens are not xeriscape-able because they require constant moisture to develop the crops. You can minimize water waste, but you can't turn them into a low-water use area.

Get a moisture meter.

You probably have adequate drainage and organic material, but you never really got the soil solidly moistened so you are dumping inadequate amounts of water onto really thirsty dirt and going nowhere.

You need to really SOAK the soil less often instead of dribbling tiny quantities onto it daily. Take a soaker hose of some sort, lay it out on the beds to get good coverage and give them a couple hours of slow soaking ... until your moisture meter is showing that multiple spots at least a foot away from the hose are wet as far down as you can stick the meter. Not damp, WET. Then mulch the heck out of the beds and monitor the moisture. When it drops to "Damp", soak the heck out of it again. Repeat as needed.

As a reference point, I have a 30x8 foot garden area on a drip system that's getting about 50 gallons a day to keep the plants happy. Granted, it's Phoenix in June, but vegetables don't tolerate drought.

Mulching is advised.

I'm in the desert where its hot and windy. Putting a few inches of lawn clippings on top of my raised beds helped tremendously.

I do some drip irrigation and also some hand watering where needed.

lazygardens' advice is excellent. Mulch and soak deeply. High water needs are one of the major reasons I don't grow vegetables in our urban Oakland hills lot. I can water (soaker hose system) once every 2-3 weeks, no more than that, and keep my garden beds evergreen and full of flowers.