Answer: Unfortunately, bagged materials including top soil and compost can be made of almost anything since they are unregulated materials. Without seeing and feeling and testing the soil in the raised bed and below it, it is difficult to make specific recommendations, but here are some suggestions that might help.
Maybe your top soil contained a large proportion of sand causing it to drain so fast, or maybe there is something else going on. Milled sphagnum peat moss is sometimes used in potting mixes and as a soil conditioner because it is capable of holding both air and water -- a bit like a dampened sponge can. However, once it dries out it is very difficult to re-moisten. For this reason many peat-based soil mixes will include a special wetting agent. Since your problem is already one of difficulty moistening the mix, I don't think is the best thing to use. (Peat humus is another material sometimes sold as a soil conditioner, but in my experience it is so decomposed that it is more like muck once it gets wet so I would not recommend that either.)
At this point I think I would recommend you add copious amounts of organic matter in the form of this fall's autumn leaves. Collect them, chop them up, and dig them into the soil along with some late season grass clippings (if they are herbicide free). Add a deep layer as the leaves will break down and decompose and the soil level will settle as a result. Next summer, use an organic mulch such as straw in your veggie garden. This will decompose and improve the tilth by adding organic matter to it, too. In this way over time you should end up with terrific soil by essentially composting in the raised bed. Also, depending on what your native soil is like you may want to loosen the soil under the raised bed and work some of it into the raised bed's soil. If it is clay based for example, the clay will help the soil hold a bit more moisture longer.
In the meantime to finish out this season, you might try adjusting and calibrating your watering practice to try to soak it thoroughly and deeply. It is usually better to water deeply less often rather than sprinkle lightly every day. Even though a raised bed may drain exceptionally well, if the soil is full of organic matter it should not dry out overnight especially with a good mulch layer and a covering of plants.
When you water, apply it very slowly over a long period. After watering, wait a few hours and then dig down and see just how far that water soaked in. Sometimes it can be very surprising. It may be that it is running off the surface and out the sides between the soil and the edging material, or it may be that what you think is a generous soaking is just not enough. If it is not soaking in at the surface, you may need to poke some holes down into it to help the water percolate through and begin re-wetting the bulk of it.
Your local county extension may also have some suggestions and should be able to help you with some basic soil tests to try to determine what you actually have in the raised bed. I hope this helps you get started in tackling the problem.
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