I wouldn't mind a stealth-assassin character. Perma-stealth shouldn't exist, but it should be a self buff or something like mist where it drains energy during use and disables during attack. Mostly I support the idea so that the other anti-stealth items would have more use.

In DOTA-Allstars, there are abilities where units will go invisible and gain a large speed increase (Windwalk).  This effect breaks when the unit attacks or after a duration.  This ability was mostly used as a very effective retreat, but also to sneak behind enemy lines.  It was considered a very impressive skill to be able to predict where the retreating, invisible hero was and snipe him with a well placed and well timed AoE to finish the job.

Some heroes go even further to deal ~2x damage on the hit that breaks their invisibility, thus having a backstab like move.  This would be used as a kind of finisher for melee heroes when an enemy was trying to run away: invis, close the gap, and stab for the killing blow.

One unit in particular, the Stealth Assassin, has a mid-game ability where he goes invisible so long as he's not attacking anything.  He's very fragile as well as a melee-type and, while annoying, was certainly not game-breaking.  While invis, he still took DoT damage or any AoE damage he may walk into.  Most players used his invis to spring on enemies that were already fighting other heroes.

Invis, even a 'permanent invis' isn't game breaking so long as the character is made a little less durable to compensate.  Then its up to the skill of the player to take advantage of the Demigod's abilities.

This would also give some real worth to the seeing eye items you can buy, as see-invis isn't so useful when the only invisible thing in the game are Regulus' proximity mines.

but there may be one problem to invisiblity

if u suck and don't have enough favor or never lvl an dget enough gold u won't be able to detect invisible DG's

to fix this the invisible DG should be able to be seen when attacking, this way they can sneak up on you and do some damage, but the other DG would still have a chance to defend without buying expensive items.

another fix is to make a faster DG with a lower DPS then UB and add like a temporary invisiblity spell and a larger damage backstab speel. this way they sneak for a littkle bit, stab and are then visible after they stab. this gives them an advantage with their low DPS and makes it a more unique type of assassin than rook(the tank/tower killer) UB(the demonic little pest that we all love and hate) regalus(the DG raper and overall badass who is only good n the hands of a moderately skilled player) and TB(who can deal instant huge damage)

i did not mean to make it seem like invisible attacking was my point, i ment one skill attack while invisible to do extra damage and after that attack happens the invisiblity breaks

however we have to remember: when building a good Demigod its not all about that one character having something that gives him/her an edge... its about the skill tree.  so if we were to have a stealth type demigod would stealth be just a branch of the tree or the whole trunk?

if its going to be a branch a simple incleasing backstab with reduced CD as you level would make sense.  maybe even throw in a slow and armour reduction for the highest level (lv 15) and you've got a pretty decent skill.

however if its going to be the tree then u'll have to split it up into offensive/defensive/supportive.  possibilities are nearly endless but having a good 4 or 5 skillz that meld together very well when taken 2 or 3 at a time can be tricky.  i'm going to have to do some hard thinking on what kind of Demigod this could build....

[EDIT]  didn't see Extacide's post cause i was typing mine up when he posted it... so Yes... i agree. if you have any suggestions on skillz this is probably a good a place as any to work out the kinks