Your downspout appears to be half buried at the bed edge. Water hits the edge and shoots back where it swirls the mulch out into the lawn. Put a brick or splash block under the end to raise it clear of the edge, or invest in a short downspout extension.

I was reading the renegade gardener.
He says this:
Do not use a landscape fabric/weed barrier under wood mulch, as it blocks the natural decomposition into the soil, and in heavy rain floats mulch placed on an incline down the slope.

It doesn't appear you have any sort of slope, there, though. I've linked the article I took the info from, below.

Here is a link that might be useful: Landscaping 101

My new neighbors decided they didn't like the rock border the previous owner had along their driveway in the planting bed, so they took them out and set them aside until they could figure out what to do with them.

Well, we had rain, and then more rain, and then more rain, and finally when it cleared up they spent over an hour sweeping dirt off their driveway, back into the planting bed. LOL

I had to chuckle, because the next day the rock border was put back in place.

I agree with a gutter extension. The water is probably back filling in that area, and mulch floats away with the excess water, but since you appear to have the same problem in the backdrop, I'm inclined to think it also has to do with your border around the mulching bed.

If I'm correct in assuming there is a plastic border in place, I'd rectify this by adding more soil in the mulch bed just along the border to make it almost level with the top of the plastic border. Otherwise, if there is too much height with the plastic vs. your soil level, you are disturbing the natural flow of the water from your mulch/planting bed into the lawn...it hits the plastic and flows back into the mulch bed.

I think scraplolly maybe onto something. Yes, there is a fabric weed barrier under the wood mulch and, yes, there is a slope, although it may not appear so in the picture.

Btw, I had a shorter downspout extension before with the same results, that's why I put the longer one on there. Obviously, it didn't work.

The idea was to put another short extension onto your existing downspout - make it a tad longer out into the grass; not to shorten it up so it dumps directly onto the mulched area.

I think what I see here is a lot of water behind the houses from backyard, roof runoff, and maybe the slope behind the lots. The water is directed to a swale between the houses and the flow at peak is high enough to get into the mulch as it rushes to the lot front.

The grass could be removed and the swale regraded deeper and more over toward/on your neighbor so that the flow level stays below the mulch. In my opinion a better solution would be to build a 4 by 8 inch curb between grass and mulch as shown in the lower part of the graphic below.

{{gwi:42076}}

I had a friend with a similar problem some years back. She spent thousands to have a large mixed border professionally installed, but the crew blanketed the entire planting surface in weed barrier fabric, cut x's in it to plant the perennials and shrubs, and then bark-mulched over the whole thing. Morning after the first rain, the phone rang -- would we PLEASE come over with shovels and help replace the mulch?

The area doesn't look all that large... I'd tear out the fabric first, if I were you. I have mulched areas on a slight slope similar to yours, and my "un-fabric-ed" mulch stays put, even during heavy rains.

I agree that the weed fabric, combined with the fact that the mulched area extends into the lowest spot in the lawn, is causing the washout. The remedies suggested above are good ones.

Another point, however, is that with weed fabric or without, mulched areas will eventually start to sprout weeds, and will require not only weeding, but also regular refreshing with additional mulch to look good. A suitable groundcover plant, once well and densely established, will cut down on the number of weeds that are able to gain a foothold, will reduce or eliminate the need for mulch, and eliminate the problem of the mulch washing out onto the lawn.