This is an interesting question. Here's why:
- 休める has the definitions of “rest; give somebody a rest” and “put {somebody's mind} at ease [rest]; give relief {to somebody}” and “stop; suspend; freeze}.
- 休む has the definitions of “rest; take [have] a rest; repose; take time off” and “have a day off” and “suspend {business}” and “be absent {from school}; absent oneself {from school}” and “cut {a class}; play truant (from school)” and “sleep” and “go to bed; retire; turn in”.
- 会社を休む has the definition of “take a rest [break] from one's work; take time off from work; I'm going to take a break from the company”.
All right, now let's look at your sentence.
明日、会社を休む。
Translation: Tomorrow, I'm going to take a break from the company.
Of course, this sentence could be translated in many different ways, but I think the gist is pretty clear.
Let's try changing the sentence like this:
明日、会社を休める。
Translation 1: Tomorrow, I will rest the company.
Translation 2: Tomorrow, I will give the company a rest.
Translation 3: Tomorrow, I will put the company's mind at ease.
Translation 4: Tomorrow, I will stop/suspend/freeze the company.
Now, I don't know if you feel that companies are people, but I think we can agree that the first three translations seem strange. The fourth translation seems to make the most sense, but it refers to something else entirely.
So, in summary, if you're talking about taking a day off from the company, then 休む is the verb for you, and if you're talking about stopping the company, then 休める is the verb for you.