I've had several items stay far, far, longer than a day in a vendor's shop before. I am not sure if they stay indefinitely, though they seem to take a lot of time to go away.
The UESP wiki lists two distinct types of permanent items:
Type 1 - Permanent (fully)
- Keep their RefID number, when dropped into the world
- Do not lose any of their persistent traits when dropped into the world
Type 2 - Permanent (until dropped)
- May keep or lose their RefID number, when dropped into the world
- Lose any or all of their persistent traits when first dropped into the world.
List of permanent items
The following items were found to be fully permanent:
- Aetherial Crown [DG]
- Ebony Blade
- The Gauldur Amulet
- Zephyr [DG]
The following items were found to be permanent until dropped (or placed on a weapon plaque):
- Calcelmo's Ring
- Declaration of War [DB]
- Eduj
- Emerald Dragon Claw
- Halldir's Staff - the one you get from Halldir's ash pile, not the one which drops near it
- Ironhand Gauntlets - looted from Hajvarr Iron-Hand
- Iron Dragon Claw
- Journals of Ralys Sedaris [DB] - all volumes
- Klimmek's Supplies
- Letter from a Friend - all instances
- Okin
- Ruby Dragon Claw
- Saerek's Skull Key - only if you do not use it to awaken Otar the Mad (awaken him with shout or rune spell instead)
- Staff of Hag's Wrath
- The Aetherium Wars [DG] - only the first copy, obtained before or during associated quest
- Torsten's Skull Key - only if you do not use it to awaken Otar the Mad (awaken him with shout or rune spell instead)
- Whiterun guard's armor, shield, helmet, gloves and boots - looted from Mirmulnir
Note: Permanent weapons may fail to prevent corpses from disappearing, although they will remain in respawning containers.