After I successfully cast this spell and hit an enemy, I can never cast this spell ever again. It keeps saying the spell fails, even with an empty hand, and after resting.

This probably doesn't help you much, but I just tested it on the GOG version of the game and it worked. Laurann, the quickstart party's mage did cast and use four shocking grasps in a row on a bunch of wolves in the beginning of the game.

After exactly FIVE casts, the game won't let you anymore. You will get "The spell failed!" without explanation.

Try it some more after resting. Or better yet, create a party of 4 mages and memorize nothing but shocking grasps. The spells will start failing before you even run out of charges.

You're right. I can confirm that after 5 castings the spell will always fail. No idea why. Funny thing though, I've played that game countless times, but never used my mage as a melee fighter and therefore never encountered that bug.

Same here. Played this game countless times since the 90s and only discovered it last week!

---EOB1---
Another cool discovery: I never saw a need to use a mage as melee fighter until this week. If you have 2 mages (I had one mage and one F/M/C), cast shield and you'll take ZERO damage from Kenku's magic missiles! You will only take damage from their weak staff attacks Getting a staff of your own for your regular mage is a must, but they are a rather common drop.

I paid close attention to the resting messages and after casting Shocking Grasp four times and then resting at the end of the rest I got the message "Laurann's Shocking Grasp spell expires." I then used the fifth Shocking Grasp spell and from then on the spell fails. When I then rest again I won't get the "Laurann's Shocking Grasp spell expires." message again.

No, the spell expires like Shocking Grasp does after your first rest and you then lose all your temporary hp (EOB2 uses a different engine than Dungeon Hack. Would be interesting to check that in EOB3, as that uses the same engine as Dungeon Hack). But also like Shocking Grasp you won't get then message again, making the spell fail after four uses. And with the first failure message you'll also lose your temporary hp.

In other words, Vampiric Touch is useless in the long run. I guess AD&D game developers can never get that spell right.

Here is the list of inaccurate implementations of that spell that I am aware of:

EOB2: Expires properly, but after the fourth use, will never work again.
Dungeon Hack: Works, but HP remains and stacks, making the spell far more powerful than intended.
Dark Sun games: Works, but temporary HP acts like healing, with the exception that your HP can go above the normal maximum (but HP above maximum is lost on the next Vampiric Touch). In Wake of the Ravager, getting HP above your normal maximum allows ordinary healing to raise your current HP without limit.
Infinity Engine games: Works, but temporary HP isn't accurately implemented; instead, the effect raises both current HP (lasts as long as ordinary healing) and maximum HP (has a finite duration). Annoyingly, the spell also makes the caster immune to it, making it rather pointless to have multiple copies of the spell memorized, while also making the caster immune to enemy uses of the spell as a side effect. Also, the spell can be cast on objects, and it occasionally bugs out and gives far more HP than was intended.
Temple of Elemental Evil: Does 1d6 + level damage (instead of 1d6/2 levels), and grants the user 0 temporary HP. (Temporary HP is implemented properly in ToEE, except for the fact that multiple sources stack without limit, allowing False Life to be stacked.) (Temple+ is supposed to fix Vampiric Touch, but I have not actually tried that mod.)
Don't know about Neverwinter Nights 1 and 2.

It just seems that, for whatever reason, developers *never* get this spell right.

Does the spell at least work sensibly in EOB1, or does the EOB2 bug apply there as well?

Vampiric Touch AND Flame Blade also have the same bug . :(
They even share the same counter: 5 casting of any one of them and it's failure forever.

Maybe that bug affects everything, that uses the caster's hand as a weapon?