... I and maybe a few of his 'other elves' may be able to help you.
Personally, I wouldn't stain it at all. You'd simply let Mother Nature gray the cedar. Then, I'd simply wash it a couple of times a year with plain, old dishwashing soap. Cedar has natural oils in it that want to 'come out'. Applying something like a stain will create a layer that prevents the cedar from 'expressing' its oil. The natural oils from the cedar will 'push up' the stain from underneath, thus, separating it from the cedar where it chips and peels. If you stain your cedar deck, you may end up doing it every year (as you are finding out.)
Powerwashing it will eventually remove the old stain. (See Different Situation for some guidance on setting your pressure washer. You may need to wash it a few times over the next year or so before all the old stain is totally removed.)
My best to ya and hope this helps.
PS: But if you insist on staining, Cuprinol is a better stain than Thompson's, and read the can FIRST (BEFORE you leave the store) to see that you understand the instructions. This sounds obvious but you'd be surprised at how much MORE you learn by reading the can ...