You just need to have held the item in your pockets at some point. You can pick it up and put it right back down and it'll be in your catalog.
Make sure to check MoriDB before you sell off your items. There's actually a good bit of non-reorderable items in this game. If the items are all from Timmy/Tommy and Able Sisters, then you'll mostly be fine. But there's still some Timmy/Tommy non-reorderable items like the lawn mower and sprinkler, as well as the fortune cookie items.
If an item is non-reorderable, it won't have a little book symbol next to the purchase price (or won't have a purchase price listed at all).
Also, keep in mind that MoriDB is wrong for some things (like it claims the turkey is re-orderable... it's not), but for the most part it's right.