Your dahlia needs an intervention! A taller stake and ample tying would help corral falling branches but your problem sounds like it would be solved easily by disbudding. Leaving only one bud to mature instead of 3 heavy ones will make for much less stress on a branch, more room for a solitary flower to develop to full beauty and less likelihood of loosing that main bloom.

On each growth tip, fold back the end leaves where buds have formed. See the main bud and slide your thumb or fingernails alongside it to carefully snap off the little side buds trying to form. Best done in early a.m. or evening when they aren't rubbery. Check growth tips the day after watering or a rainfall as those little buds develop fast.

That should help, I think. Below: leave the center main bud alone, scrape or break off the side buds so it looks similar to the blurry second photo. Sometimes, depending on variety, the side buds are staggered up and down the stem a bit, but should still get removed for best flower development and weight reduction on the stem.

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Here is a link that might be useful: Disbudding

Thanks much! I hadn't thought of that. Shows how new I am to the whole plant thing :-)

Thanks again. I tried this today and was shocked at how many of those little buds I found. Now I think I stand a chance of keeping the blooms on the plant.

You're welcome. Disbudding is a constant thing and should make a big difference in the weight on your branches, better main bloom and longer stem on that bloom, if you cut them.