What happens when Mathas, Fiend Seeker's bounty counters go away and come back again?

Question

Mathas, Fiend Seeker is a new Commander card with this ability:

At the beginning of your end step, put a bounty counter on target creature an opponent controls. For as long as that creature has a bounty counter on it, it has “When this creature dies, each opponent draws a card and gains 2 life.”

A Gatherer ruling clarifies I can pick the same creature multiple times, and it stacks:

If Mathas’s ability resolves two separate times targeting the same creature, that creature will have two instances of the triggered ability. Each triggers separately when that creature dies.

This regularly means I can pick the same creature three times, and when it dies, each opponent will draw 3 cards and gain 6 life. (The extra bounty counters are redundant -- it just needs to keep at least one.)

However, what happens to those triggered abilities if all of the bounty counters vanish, and then later the same creature is bountied again?

Let's consider this scenario:

1. I place a bounty on someone's Charging Badger. It gets a bounty counter, and acquires a new triggered ability: “When this creature dies, each opponent draws a card and gains 2 life.”
2. Someone else plays plays Aether Snap, Thief of Blood, or Vampire Hexmage — the bounty counters vanish. If Charging Badger dies now, nobody draws cards or gains life, that's OK.
3. When it's my turn again, I bounty the exact same Charging Badger a second time. It gets a bounty counter, and acquires a new triggered ability (again): “When this creature dies, each opponent draws a card and gains 2 life.”
4. That Charging Badger finally dies.

How many bounties trigger then? Do we draw 1 card and gain 2 life (from one bounty), or draw 2 cards and gain 4 life (from two bounties)?

I can see this mechanically working out two different ways and I'm not sure which one's accurate:

• We draw 1 card and gain 2 life: in step 2, the Charging Badger's bounty triggered ability vanished. In step 3, it gets one back, but it's as if it's never been bountied before.
• We draw 2 cards and gain 4 life: in step 2, the bounty triggered ability just became sort-of-not-there in some way. In step 3, when the Charging Badger gets a bounty counter again, the previously-there triggered ability also comes back along with the new one we just placed there.

Answer 1

The bounty will only trigger once.

For as long as that creature has a bounty counter on it..." is a continuous effect.

The effect itself being that it has the triggered ability, and the duration being "as long as that creature has a bounty counter on it".

611.2a A continuous effect generated by the resolution of a spell or ability lasts as long as stated by the spell or ability creating it.

The moment the first bounty counter leaves the creature, the continuous effect ends, and thus it loses the triggered ability. The fact that it later gets a new, second bounty counter is irrelevant to that first ability.

It's worth noting that if you give the same creature 2 counters, and then it loses just one of those counters (such as through Medicine Runner or something), then it will still have 2 instances of the triggered ability, because neither continuous effect will have ended.

Answer 2

You would only draw one card and gain two life.

The key part is in the description of Mathas, Fiend Seeker's ability (emphasis mine):

At the beginning of your end step, put a bounty counter on target creature an opponent controls. For as long as that creature has a bounty counter on it, it has “When this creature dies, each opponent draws a card and gains 2 life.”

When you remove the bounty counter on the Badger it loses the "When this creature dies, each opponent draws a card and gains 2 life." ability. So even though you might put another counter on it again later, the game treats it as never have had the ability in the first place.