Do Heirlooms reset every Reign?

It's nuanced, and worth understanding properly:

• Unlocked Heirloom upgrades are PERMANENT — they never reset. The gold and currency you put in are kept for life.
• The Mastery bonus (one per upgrade rank) is always active, independent of everything else.
• BUT: a Heirloom buff is only active if your House Level is high enough, and House Level resets every Reign.

So in practice: you never lose a Heirloom you bought. However, at the start of each new season, some of its buffs are "switched off" until you've re-grinded your House Level. The right practice: invest in the Heirloom once (permanent), then climb House Level quickly each Reign to switch the buffs back on.