Been playing the HH since MH2. Mostly it is time based. If you do successive Healing, it has a reduced chance to do a higher effect. If you do it sparingly, it almost always does the full effect.
I may be off, but from my playing, there is about an 80%+ chance to get the full healing effect (with maestro) when done a few minutes apart. If you are just spamming the song, it is about a 20% chance that it will trigger the full healing effect. And this is cummulative as well. Meaning, if you have more than one HH user, the moment you are hit with a song heal, you are already running diminishing returns on your own healing songs.
IMO, you shouldn't rely on the HH to be the end all skill nullifier in the group. Learning how to dodge, specially moves that are very telegraphed like the Giggi poison, is your best bet for being a better hunter. Now for those occasions that there is a unavoidable poisoning, then the HH can and will be a life-saving addition.
Treat the HH as a splint to help in the group's shortcomings, not a bulletproof vest. Or use it as a method to increase the groups overall effectiveness, because it certainly is not a bazooka. The HH is effective for:
1) Exhausting a monster
2) KO a Monster
4) Breaking Monster Parts
5) Preventing status ailments
6) Removing the small hits from the wreckless big hitters
7) Increasing the groups' damage/defence, increase total health
You can focus on only a few of these things at a time, since not all horns are designed alike. The Brachy horn, for example, is made to be mostly all out attack on your part. While it's songs can do things like: Increase elemental damage, prevent mud/snow, tremors, increase dragon resists, sonic bombs and the like, most people do not have problems with these ailments. The great bagpipe, however, gives Attack, Defence, Max Health increase and negates all wind; when your group is fighting any monster, this HH should constantly play it's tune whenever they go down. Its attack is not among the highest, but it more than makes up for it in the group's overall output.
Bah... I talk too much. Hope some of this helped.