I correct student mistakes when providing grammar content to them. I frequently encounter the word "English" in e-mail situations and it is not capitalized. I just need some clarification. Thanks in advance.
Yes, it always is, except sometimes when it is used (chiefly in American English) to mean putting a kind of spin on a ball in games like pool.
I think one of the reasons you see it without a capital is that in some languages (certainly French) national names are capitalised when they are nouns (l'Anglais = "the English person") but not when they are adjectives (un livre anglais = "an English book")
Alternatively, it might just be that people don't think it important in the contexts where you've seen it.