Growing herbs

sounds like they are probably getting watelogged, do you have enough drainage in the sink?
what type of soil/compost do you have in there?
you really need to elaborate a bit more with what you do to them...

Me too! I planted Lavender, Rosemary and Thyme. About 6 weeks ago. The Lavender and Rosemary are thriving but the Thyme has shrivelled turned brown and died.

Good drainage is essential for most herbs - I planted lavender last year and even though they were planted each on its own mound of soil to ensure good drainage, I still lost a few over the winter.
I would empty the sink and fill the bottom couple of inches with crocks, stones and polystyrene chips (or broken up polystyrene packing) then add more compost with added grit to improve drainage. Then replant and make sure the plants are not too deep. Cover the top with slate chippings or stone to keep them dry and water only when the soil is dry - oh, pull the plug out too (LOL)

I wonder which herbs you're trying to grow - a belfast sink would probably be okay for chives, thyme and possibly sage as well, but the others, like fennel, rosemary, lavender all want more room for the roots than the sink would provide; others like oregano and marjoram want to spread out and take up a large space, say 1/2 feet, so not suited to growing in such a small receptacle.

It's probably keeping the soil too moist. a sink is for holding water after all. You should be successful with the moisture loving herbs such as parsley, lemon balm, mint. Or empty it and mix lots of grit with the compost and put a 3 or 4 inch layer of pebbles in the bottom.

A lot of herbs are from the Mediterranean region so need free draining soil, quite poor, lots of light and air around them and probably a mulch of pebbles to imitate their natural growing conditions.