You can solve your problem by using mulch. Add 3-5 inches of mulch to your raised bed. Chipped wood mulch might be best. That free stuff from your county is good too. But do not mix it into the soil. A thick layer on top of the soil will retain the moisture, prevent weeds, break down into slow release fertilizer/compost, and might well solve every imaginable problem you are having.

I suggest you watch the video as shown below. Good luck!

Here is a link that might be useful: Mulch saves the day every time.

You've filled your beds with a soil-less mixture that might be better as a potting medium. It's so porous that water evaporates quickly. The mulch idea is a good one, but over time you might want to add some soil to the mix (next time you plant or till for example). You'll need to add something anyway because the compost and peat will decompose some and the level will sink. So when you fill it back up use topsoil or garden soil.

"all 8 inches"
Are you saying that your 4x12 beds are only 8 inches deep.
5 gallon bucket would work better.
I put in the first raised bed for some friends this Spring.
The bed was 4' X 13'(the length of the boards), I tilled the soil down 6-8 inches, removed all the loose soil & roots, broke up the bottom & put down 1/4 inch wire/hardware cloth to keep pests out. Covered the wire with 4 inches of soil then mixed soil & coffee waste compost, pine bark fines that they had on hand. Once the bed was level we put in untreated 4x4 post
& put up 2- 6 inch boards on all four sides & filled in with more compost,soil & pine fines. This was a total of 14- 16 inches with room for adding compost after each growing season & mulch.
IMO you should have at least 12 inches of loose soil/compost & 3-6 inches of mulch.

msarro, If you have some half-way decent soil under your soil-less mix, I would take a potato fork and dig some of that under soil loose to be tilled into your mix.

You are not getting that organic matter wet, so the water you are appying is simply flowing right through. There is probably too much vermiculite, used to promote drainage, and the compost and peat moss both can be hydrophobic until they are thoroughly wet. I have seen compost that would not wet unless it was put into a container which would be filled with water and left several hours until the compost did soak up the water. Peat moss the same, it can take several hours before the peat will absorb water.

I think kimmsr is on track about the water flowing right through. What I do with containers using a peat-based mixture, when they get really dry, is to water them well (most of the water will flow through, but a little bit will stay), wait a while, then water again. The water "sticks" better the second time around, after a small amount of water has been able to absorb. It's got to get a foot in the door, so to speak.

For a pot, I might wait 20 minutes. For a large bed, you might want to wait longer...but not all the way until "next watering time." I'm going to guess an hour...but hey, maybe 20 minutes would still do the trick. This is a big guess. You need to get the water fully absorbed, and then never allow it to fully dry out...or you'll be starting from scratch again.

Drip irrigators?

In decades of gardening, I've never had a circumstance where peat and/or vermiculite did more good than harm (not including containers). The situation will eventually work itself out, but my policy is to never add anything that mother nature wouldn't. "Good soil" just takes time, kudos to you for getting started!

Assuming the raised beds are directly on the ground, the plants will soon get their roots down into the - clay? - and be better able to withstand dry conditions more easily then. I would mulch too. A finely shredded wood, so it helps add tilth to your soil by decomposing quickly.

Growing veggies is not the easiest thing to do, you'll have lots of learning experiences. For example, even if it goes right, it can go wrong. About 12 years ago my daughter planted watermelon seeds and I didn't pay any attention to the package. One of the vines grew a melon but it stopped growing long before I thought it should. After about a month of waiting for it to get bigger, it never did so I cut it off and sliced it open. I was so disappointed to see that it was orange inside and hadn't even made any seeds yet. I thought it was poisoned from the neighbors lawn service (heavy rains would cause a flow from their yard into ours) and threw it on the compost pile. The next spring I was looking at veg seeds and saw a package of little round ORANGE seedless melons. Well duh, I didn't know there was such a thing. I probably threw out the best edible thing we grew that whole year! I think the curse of the scorned melon was finally lifted last year. Mother nature let 2 little melons ripen enough for us to eat but not get torn up by squirrels.

Good luck, keep trying & have fun!

I can tell you, that the soil not retaining water was my big complaint about "Mel's Mix." When I used that, there were days in tsummer I would have to water 2 times a day, not a wise proposition in the desert. Now, I just amend my native clay with peat, compost and some vermiculite. Clay holds water remarkably well, vermiculite helps the texture as does compost, and the peat helps my very alkaline soil and the tilth as well. If you have plants already growing, I would mulch really well this year and then at the end of the season add soil.