Let's go over the basics first.
1. Do you fulfill the difficulty requirements? You can only heirloom stuff you can use, so no looming horses without riding, bows without PD or weapons your not strong enough to use.
2. Is your inventory clugged up? If you got too many items (95ish or above by my experience) then not all will show up ingame and it might be the same for the heirloom screen.
Regards,
Jarlek.