I put (Behr-Home Depot) deck sealer on the exterior of my coop and it lasted ONE winter. It peeled up immediately in spring. Had to be sanded off - what a mess.
Now I used plain ol' Linseed oil, mixed 50/50 with mineral spirits. It soaks right in, dries in a day (quicker if the weather is good) and lasts through the harsh winter. I re-coat every spring. Paint it on (it's thin, but sticky), let it soak in for 15 minutes and wipe away any residual. Honestly, on my coop, there is never any residual - it all soaks in. Sometimes I put on two coats. Takes about an hour for my 6x8 coop, so not bad. It seals the wood from moisture and gives it a natural, clear stain. I've been treating my teak patio furniture with this same mixture every spring for 12 years and it still looks good as new.
ETA: I didn't go cheap, but I certainly could have spent more. Maybe the coop is just too exposed to the elements? Maybe it didn't absorb enough after the stain was applied? Don't know. Either way, I won't make that mistake again.