I think there are a few reasons he keeps it.
First, like
@Phil Ken Sebben said, it hides his mouth. I don't think it's irony, though; I believe it's deliberate. Remember, Russ believes he'd be a hot guy without his disability, so he's trying to hide the most visible symptom of his disability.
Second, he likes to pass himself off as "studly." It's part of the reason he works out and brags that he's a paralegal and that he worked at a law firm once. He thinks it makes him more attractive; the beard, I believe, is kept for the same reason. Manly men have beards. Russ has a beard. Therefore, Russ is a manly man(let).
Third, he's lazy. We've already established that he puts in the minimal effort for everything. He already puts in the bare minimum for hygine; why should his beard be any different?
Fourth, his priorities are fucked up. Why should he waste money on a trimmer or going to a barber? That's less slot machine and hooker money for Russ!
Once upon a time, though, he did try to keep his appearance neat. Probably due to his parents or the church leaning on him.