Wrong soil. It is too rich and keeps the plants too wet. These plants need lean, well draining soil.

FataMorgana

I'd suggest taking them out and replacing at least a third of the soil with a coarse sand. Add some perlite if you've got it, or grit, anything to improve the drainage. Some people grow sage in commercial mixes designed for cacti.

It's a little difficult given your humidity levels, but try to keep the soil pretty dry. Keep sheltering it from excess rain, like you've done, but make sure it's in a place where it gets heaps of sun.

What's the pot size? Both sage and rosey are really small shrubs that can grow large when happy, and sage will need lots of root space. I would recommend separate pots. As mentioned, the mix is probably rich. I do mix succulent or bonsai soil in with my potting mix for both plants.

How much full, direct sun are they getting? The sage looks a bit leggy to me, but it could definitely just be the variety or fact that it's potted. It's also not unusual for some of the larger leaves to brown and fall as new ones come in.

My sage plant is more than 15 years old and grows like crazy, flowers seed themselves and I get the baby plants to share with others. LOVES it hot, sunny and dry. Rosemary same thing. I have both in the garden where the soil is poorer to coarse. Up against a sunny fence or building protects them from excess rain. Only wish up here in zone 5, my rosemary would be perennial, but is only when the winters are sunny and I mulch and cover them. Do you dry your herbs for future use? I love to give all my friends and neighbors sage cutting bouquets, especially for the holiday season for when they make their turkey stuffing.

I also think re-potting them separately would be a good idea.

If it were me, I'd use a knife and nick or scrape most of the stems near the bottom. I might even apply some rooting hormone powder to the place I scraped/nicked. Then, I'd bury it deeper, with potting mix covering the scraped/nicked areas on the stems. Give it a couple months, and you could carefully dig things up. If the branches have rooted, you can cut them away from the main plant and have more plants that way.

Also, rosemary and sage need really good drainage, and really don't need as much organic material and fertilizer. I add sand or perlite to 'potting mix' for rosemary and sage, about two parts potting mix to one part sand and/or perlite.

You can also use commercial "cactus potting mix" if you don't want to mix your own.

I personally would opt for a bonsai soil mix rather than a cactus mix or adding sand to a standard potting mix. Bonsai mixes are designed for woody plants.

FataMorgana

Interesting, I didn't know sage likes it dry. The previous owner of my house planted it everywhere and it grows like crazy with little care, in my sometimes soggy climate.

I live in Western NY and the soggy climate doesn't hurt it so long as the site for planting is well drained. Plant in an area where water pools and it is certain doom for the plant.

FataMorgana