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