In Scotland we make a kind of fudge that is deliberatly hard and crystallised known as Tablet. This was a popular treat when I was growing up. Essencially the recipe for tablet, soft fudge, toffee and caramel are quite similar. The difference is made by how you cook and treat the mix as it cools.
Essentially you need to know about sugar boiling points. There are two important levels used: soft boil, and hard boil. My cook books suggest using a sugar thermometer to get the perfect boil but I've never found a sugar thermometer in the shops. Instead I rely on a great deal of practice, the colour, the texture and the drip of the mix to gage how hot the sugar is.
In a soft ball (234–240 °F or 112–115 °C), if you drip the mix onto a very cold surface or into cold water, then touch the drip with your finger, it will be soft like caramel. Additionally the colour will change from cream to yellow/tan.
In a hard ball (250–266 °F or 121–130 °C), dripping again onto a cold surface or into cold water, then touching the drip with your finger, it will be firmer or even hard. The colour will darken slightly to a dark yellow or light brown.
For caramel and fudge you go to a soft boil then cool. For tablet and toffee you go to a hard boil.
The next part is the cooling. This is equally important as the boiling. The faster you cool the mix the smaller the crystals become. The slower, the larger. If you want a caramel or a toffee, you must avoid agitating the mix as it cools. For fudge you should stir the gently as it cools slightly before pouring onto the try. For tablet, the mix should be vigorously stirred until stiff then poured onto a try.
It's a somewhat long shot, but if I were you, I'd give it a try again, using another form of vanilla (maybe precook a pod in the milk, then scrape out the seeds and add them), no corn syrup at all, and pay attention to using sweet butter, not cultured butter.
Fudge is all about forming the right size crystals in the supersaturated sugar solution. From your description, no crystals form at all. This could happen if you inadverently invert your sugar (= split it into glucose and fructose). In home cooking, this is usually done on purpose with acid when making non-crystalized candy. So, just in case that either your butter or your vanilla extract contains some acid, I'd use the versions guaranteed not to have any, vanilla pods and sweet butter. It's not sure that they are doing something wrong, because butter in the supermarket is rarely cultured, and vanilla extract doesn't contain acid normally, but it's better to make sure.
On an industrial level, invert sugar is created with enzymes. While corn syrup starts out as starch and not sucrose, I can imagine their enzymes being able to split the fructose off the sucrose in your sugar too. I don't know what they do to the syrup exactly, and maybe the heat will deactivate the enzymes anyway, but I think it is worth a try to make it with pure sugar, so there is no source for enzymes to land in your fudge and invert it.
If none of these is the culprit, then I'm afraid the next likely explanation is the mechanics of the beating. But maybe it's not about the hand vs. mixer beating as such. It's possible that you've been stopping too early, or that changing the attachment used for beating will change the outcome.
Best Answer
If you live at any altitude other than sea level, you may need to adjust your recipe's temperature. If you live in the mountains as I do, that temperature may vary enough to mess up your recipe, even if you've checked the boiling point of water just prior to starting the candy. The air pressure up here seems more volatile than it was when I lived at sea level. Maybe that's just because one usually doesn't get up to much candy making if there's a hurricane coming in.
At any rate, here's a link to the Unviersity of Utah's The Art of Candy Making. It has a chart on page three that will help you adjust your finished temperature (if that should happen to be your problem). I hope it will help.