I'm generally cautiously optomistic about balance problems when I first notice them.  Afterall, most times something looks imbalanced is right after it beat you, or you think that it beat you. Maybe it wasn't unbalanced, so much as you were just sucking?  Anyhow, I've kept my eye on the Heart for a while now, and I really think it is the worst effect on the game, in the game.

First, a few anecdotes:

1. Erebus chases someone all the way back to their health crystal trying to kill them, (failing, I might add).  First he goes into mist form for a second.  Then when he pops out of that, he activates Heart of life + Orb of defiance for 5 seconds, healing 1500 health and 2250 mana.  At the end of that 5 seconds, he bat swarms away.

2. 3v3, one player is Oak, and all of his team has the heart.  At level 7 he gets his 6 second long invuln shield.  Every time he invulns an ally (He or another) they also regen 1800/2700 health and mana.  MID combat no less.

These are both two extreme abuses of the heart, but let us talk a bit more about it's impact without any truly killer combos.

The most important starting point is to remember that Demigod is, at its core, a 'zero sum' game.  That means as one team gains strength (Generally via kills, or staying in a lane longer) the other team is weakened (Dying = less time to get money/xp, and getting chased from a lane means the same).

As most people know, this is part of the reason rage quitting occurs: You dig yourself into a hole, and quitting doesn't noticebly increase your chances of failure, so you do. In ANY game where this can happen, the game balance MUST be very careful not to TOO strongly award bonus' to temporary, or short term victors. In general DG does this by making the truly game winning items cost a whole heck of a lot.

The problem occurs though in about the first 5 or 6 levels.  If you get a fairly decent early advantage, maybe a kill or two, maybe getting to farm a lane a bit better, you will get to about 4000 gold noticeably before the other team.  This is also when you can pick up your heart of life.

So now that we consider the heart of life in the game combined with the fact that we are already doing fairly well, what does it let you do:

1. Stay alive longer. Even without any invuln shields, you still can duck behind a tower to heal up almost completely.

2. Stay in a lane longer.  Since you can keep at full health/mana, you can generally drive opponents from the lane, denying them XP and GOLD (And warscore) thus further cementing your victory.

The combination of these two effects strengthens any existing lead out of proportion, and very quickly creates a landslide effect.  Further more, in general the item acts as the strongest regenerative effect in the game, and is not a consumeable. It regens both health and mana, does so passively and in burst, and the price point for it is such that it impacts the early to mid game the strongest (When the team with the advantage can get them, but the other cannot).

Too Long; Didn't Read version:

1. Heart Helps a team with an advantage, press that advantage strongly

2. Heart's price point places it at a point in the game, where an advantage shouldn't be decisive. (Compared to, say, Ashkandor).

3. Heart trivializes most other health/regen items.

4. Heart combos in truly broken ways with invulnerability effects.