The progression of this quest is
1. build the 3 items for the post office
2. talk to the murmurs who tell you to look for Postmen
3. talk to the postmen (there are 2 - Robin and Wren
4. the day after you talk to the second one you get mail telling you about the VIP merchants and Leif should have both the airship anchor and the shipping catalog and station in the store.
If you did all those steps and the item still hasn't shown up in the store, you might want to double check to make sure the tiers are all completed on the sign. The Post Office items will bump it to level 3. Make sure you scroll through the list to make sure an item is missing.
If the store is complete, you could try breaking the sign, putting it back and then check after a couple days. Even hanging on to the sign for a couple days after breaking it might help to force it to work. If that doesn't help you might have encountered a bug. It isn't one that I've seen very often. You could try verifying your files too. If you have mods, you'll have to reinstall them to get them to work again.